An article in the Onion from 1907 reported that a record breaking number of American children are staying in school beyond third grade. They are learning advanced skills such as multiplication, which we are told, is a powerful form of adding, resulting in numbers so large that three or even sometimes four figures are required to write them.
My 7th grade algebra teacher would only whisper of dividing by zero because it would “upset the calculator gods”. He was one of my favorite teachers ever.
@@coulombicdistortion1814 Here's the thing about multiplying by zero: anything multiplied by zero is zero. So 0(1/0=2/0) (1*0)/(0*0)=(2*0)/(0*0) 0/0=0/0
Travis Ryno I have been stuck on this since last evening. My 13 yr old told me exactly this, and then used Banach-Tarski model to say that 1+1=1 is mathematically possible. I don’t know right now whether to believe his hypothesis or continue to say x/0 is undefined.
For the "why does it return Error in a computer" question, the division assembly instructions (at least for x86) are designed to generate an interrupt when the divisor is zero. In other words, they are told to error out.
@@Xnoob545 Presumably it would attempt that forever. It'd never find its result, and the part that tells it to stop has been chopped off, so it'll just never stop
@@Xnoob545 cpu would hang at 100% usage trying to compute the result of what cant be computed, until you restarted it. therefore safety instruction/lock was added to prevent such.
Now, I had always been taught that X/0 was "undefined", while 0/0 was "indeterminate". The logic behind this is that the denominator (or "divisor") should always be able to be made equal to the numerator, by multiplication with some factor. So, for example, 1/2 = .5, thus 2 can be made equal to 1 by multiplication with.5. However, in the case of X/0, there is no factor that can make 0 = X, since 0 times ANYthing is always 0. So, there is no correct answer, therefore, the problem is "undefned". On the other hand, in the case of 0/0, literally ANY factor will make 0 equal to itself, so there is no INcorrect answer. Thus, in essence, any value is equal to any OTHER value, which is impossible. Therefore, the problem is called "indeterminate", since one cannot determine what value best solves the problem.
I know you said this is what you were taught, but it bears mentioning that this is just incorrect. There is no such a thing as "indeterminate" in mathematics, and people need to stop using this word forever. 0/0 does not exist. Period. That is all there is to it. And there is a very simple reason it does not, but it just has to do with what division itself is. Division is just multiplication: multiplication by the reciprocal, to be exact. 0 has no reciprocal. So one cannot divide by 0.
@@angelmendez-rivera351 because in calculus, 0 is not exactly 0, 0 can be 0.0002 or -0.00001, numbers are not exactly their values. That’s why there is indeterminate
@deaf I fail to see how those points connect. 0*x = 0 for all values of x is a true statement. I don't see how this implies that 0/0 = 1 any more than it does any arbitrary number.
@@angelmendez-rivera351 Yes, in terms of numerical value, indeterminate forms are considered undefined. But they are very useful in calculus because of how they affect limits. (f(x+h) - f(x))/h = 0/0 when h=0, so it's undefined. But the limit as h approaches 0 is very much defined (when f(x) is continuous), and is in fact the definition of the derivative. If 0/0 is just undefined, derivatives don't exist, and calculus doesn't work. That's why we have indeterminate forms, at least when working with limits
An accountant, an engineer, and a mathematician are asked how much is 1 + 1: Mathematician: "1 + 1 is 2 and I can prove it" Engineer: "Well, 1 + 1 is anything between 1.8 & 2.1" Accountant: "It depends. How much do you want 1 + 1 to equal?"
There's a video around of an old mechanical calculator which gets stuck in a loop when trying to divide by zero, and the operator has to press the abort button to stop it running. Nothing bad happens - it just keeps subtracting zero and counting how many times it subtracts zero and it never finishes.
I think it's implemented at OS level. And older operating system just tried to subtract 0 from the number forever, forcing you to turn off the power and turn it on again.
@@DanCojocaru2000 If you actually think that applications call the OS to perform calculations then you haven't got a clue what an operating system actually does and doesn't do. Division is not a system task, it can be performed by any application that is directly using the processor (CPU) at user level. Actually, most CPU's have division build right into them...sometimes incorrectly, check the Pentium bug (for floating point division).
Edit: I made a mistake in my original post, and I apologize. A divide-by-zero will return a "not a number" (NaN) result for a floating-point division. I don't know off the top of my head what result an integer division returns - this is something I should either look up or simply test - but the divide-by-zero register is still set, which can be queried to determine if an exception should be thrown. Floating point values may contain infinity and negative infinity as actual values, and if you want, you can treat a divide-by-zero as infinity, and I have in fact seen API's that do this, but generally speaking, you don't want a divide-by-zero to ever be a valid operation. Original post: @@majormalfunction0071 Intel CPU's will happily divide by zero and return either infinity or negative infinity, depending on the sign of the operation - they also differentiate between zero and negative zero; the sign is simply a bit in the return value. They will, however, as Number_055 noted, also set a "divide by zero" register notifying the application requesting the operation that a division by zero occurred, which the application may then treat any way it likes, including treating the operation as an exception and possibly crashing itself. I wholly agree that "infinity" is not a valid return value for a divide-by-zero, but the IEEE standards committee had to settle on something that would work from a technical standpoint.
And that all the while glossing over X^X for negative X looking really strange (it's jumping all over the complex plane and is basically discontinous everywhere). That is not a function for which you want to find a limit. The complex version must be just as bizarre.
Do not touch the operational end of The Device. Do not submerge The Device in liquid, even partially. Most importantly, under no circumstances should you divide The Device by zero.
There's some great footage on RUclips of mechanical calculators, oldschool ones, dividing by zero. No programmed-in "Math Error" there, the things just spin forever making a racket, they're probably subtracting zero over and over but maybe some of them are failing in a more clever way.
6:10 Yes, computers are taught not to divide by 0. The reason is because bitwise math operations are only add and subtract. Multiplication is just repeated adding, while division is repeated subtracting. If you divide by 0, you are telling the computer to subtract 0 from the original until the value of the original is
@@jathebest2835 That doesn't matter since the sign of the quotient is determined by the dividend. So are you going to get it as infinity or negative infinity? Since the answer is undefined anyways, is there a point in computing it?
Multiplication and division are the next iteration of addition and subtraction. The iterations beyond those are exponents and roots. When you get beyond that, it gets really hairy. Layered exponents (also known as "towers") and roots (just the reciprocal of towers) are as far as most people dare to go. But you can technically go as far as you want, and Knuth invented a special notation to explain the weird realm beyond layered exponents/roots. It was used to create one of the largest numbers ever conceived, Graham's number.
When you asked the old Sinclair calculator from the 70s to divide by zero, it actually tried! It would give you multiple answers one after the other until eventually it spat the dummy, showed all the decimal points and locked the screen.
I consider 0/0 to be a feature, not a bug. Simple Algebraic Rearrangement tells us: If Anything * 0 = 0, Then 0 / 0 = Anything. Intuitively, 0 / 0 represents the question "what number can you multiply by 0 to get 0", to which the answer is clearly "Anything".
MumboJ the square root symbol like that that is a function. when you use the square root symbol like that you are taking the principle root which is always positive. You mean to right x^2=1 which has to possible solutions that make that statement true. If you want the negative value you have to put the negative sign in front.
Which is exactly how 0/0 works. It is a rearrangement of 0x=0, to which anything is a solution. Function Symbols are often used to represent this concept, and the phrasing I used was not incorrect.
MumboJ a square root of a number can be either positive or negative. Its because both positive squared and negative squared are positive. Example: √1=±1 √4=±2 √2≈±1.414
in high school I was doing a problem on the blackboard in an algebra class and I was finishing it fast so I was writing both sides of the equation (my way of doing it) and the teacher saw it and yelled "algebraic sacrilege!!!!" and that scared me lol and everyone else in the classroom. I swear that we almost hear thunders falling on us. Sufficient to say that I never had the opportunity to explain to him that I was still writing my answer, so I just completed the answer as a "correction".
@@circuit10 I meant that when you start writing it, you begin with the right side, you finish writing that side and then move on to the right side. I was doing both sides at the same time.
The computer is actually taught to not divide by zero. There are many situations in software where dividing by zero is caught and protected against. My brother used to work in a hardware store and he had a computer that gave a 'divided by 0' blue screen. According to the story, he laughed insanely laud at that blue screen. Usually that doesn't happen but the computer had a defect RAM which fed corrupted data into the processor as it fetched the information to execute the micro programs. The processor actually had a build in protection to prevent dividing by zero, it stopped the operation and 'breached' away from its micro instruction to the error handling of windows which on its term showed the blue screen. In short, the computer doesn't even attempt to divide by zero. If you were to try and do it it would probably try to apply a form of implemented long devision which would obviously fail and I have no clue what it would return.
Robert sorry RUclips isn't letting me post my own comments one thing I would note for the people at number phile is it's as easy as defining 0*y=0 y in the complex plane but not =0 so 0 divided by 0 makes no sense since you can turn it into y*0/y1*0 the 0's can be seen to cancel and then you get y/y1 for any values y,y1 and therefore can take on any of any infinite values.
***** Actually, I think that algorithm doesn't quite simulate a division by zero because, for any value you insert as a divisor (if you swapped "int(n) - 0" for ,say, "int(n) - 3", for example), you'd still have an infinite loop (because the condition for the while loop will always be true and there is no condition for it to actually stop). A true general algorithm for a division of integers would be something like that: ----------------------------------------------------------------------------------------------- n = int(raw_input("Insert the dividend: ")) m = int(raw_input("Insert the divisor: ")) c = 0 result = n while True: result -= m if result < 0: remainder = result + m break c += 1 print c print "%d/%d = %d with a remainder of %d"%(n,m,c,remainder) -------------------------------------------------------------------------------------------------- If you insert 0 as the divisor, the "c" values will explode into infinity on the screen until you hit that close button, however, inserting other positive integer values would return normal division results. :D (also written in Python, because screw it, i'm on that lazy train too \o/)
Robert Dividng is reverse of multiplyin so: 4/3 is 4 * (1/3) and a proof of this is that: (4/3) * 3 = 4 (a/b) * b = a so: if b = 0 and a is any N then a =/= a which as answer is not in set N because any a in this set is equal to itself (4/0) * 0 = 0 ==> 4=0 The result of this nonsene came from the set. Any result on the corpus of N must result in the corpus of N and 0 is not in even in the set of N.
Robert Fennis Set dosent include result. Need a larger set with algebra over biger corpus with a diferent ring and more dimensions. And of course problem is solved, directX is working perfectly without gimbal lock on this wee issue of dividing by zero.
6:25 totally agree with that. I know that when I do a really intense calculation on Desmos, the calculator displays to me a message saying "definitions are nested too deeply"
I met this channel a while ago, when i was in highschool and used to watch every video. Now, as i'm graduating in mathematics i come back and rewatch the same videos, but now in a different perspective. Numberphile was one of the main reasons i decided to study math in college, despite all flaws.
From the software engineering perspective I'd say that I highly doubt that any commonly used calculator uses iterative process to get an answer for X/0. It's just a check in the code: if operation is division and second argument is 0 then print "Error". So, the first guess is much closer to reality
Definitely more likely. Calculators only really do addition and subtraction so if you tried to divide by zero it would keep subtracting by zero an infinite amount of times, just like they demonstrated in the video. Its gotta be programmed to check for a non zero number to keep it from entering an infinite loop, that seems like the best solution
It's normally an exception, stopping your execution. If you have a divide by zero in your equation and you don't stop, you're in la-la land. CPUs handle integer division (which give division by zero and overflow), languages have standard libraries for floating point. The standard is to have zero, NaN (Not a number), Inf, and -Inf as distinct results. Most calculators now have this as well (processors are very cheap). NaN is different than infinity. Infinity normally means it encountered a number which exceeded the maximum value (e.g. 300 factorial), and infinity times zero is zero. Any math operation using NaN gives you NaN as a result. You also can have exceptions for overflow/infinity, and there may be cases where you want to know when you underflow (if you have x and y, which are not zero, but you get zero because the number is too small.. that's not normally one you worry about). A difficult problem in programming is when you have a one-off problem, where it goes into la-la land, and takes a few steps before it dies. Math is one of those things.
Unless someone forgets to tell the computer not to attempt the subtraction, in which case the computer may crash, which happened to an American warship, computers down for a day
Here's a simpler explanation of why n/0 is impossible and 0/0 is undefined. I use it in my 6th grade classes in Italy using numbers instead of letters. 1) division is the inverse operation of multiplication. Calculating a/b means finding a number (let's call it "c") that multiplied by b gives a (in other words, c*b=a is basically the same thing as a/b=c, you're just reading it backwards. For example: 6/3=2 and 2*3=6 are basically the same thing, you're just reading it backwards). 2) if b=0, then you get a/0, which is impossible because there's no number that multiplied by 0 gives a. In fact, a/0=c means c*0=a, and there's no number "c" that multiplied by 0 gives a. Since the operation a/0 doesn't have a result, it's impossible. 3) if a=0 and b=0, then you get 0/0, which is undefined because any number multiplied by 0 always gives 0. In fact 0/0=c means c*0=0, which is always true, no matter what number "c" you choose. Since the operation 0/0 doesn't have one single result (it has infinite results), it is undefined. I hope this can be helpful.
But all division does is count the subtractions that took place to reach the number. Therefore, it isn't infinity or the number you started with. It's 0. 20 / 4 = 5 (Five Subtractions) 20 - 0 = 20. No subtraction took place. 20 / 0 = 0 (Zero Subtractions)
@@Vespyr_ No, that is horribly incorrect. Firstly, that is not how division actually works: division is not repated subtraction, and multiplication is not repeated addition. Secondly, even if division did work that way, your answer is still wrong, becaue 20/0 would be equal, by your definition, to the number of times you have to subtract 0 from 20 to achieve 0. The problem is that, even if you subtract 0 an infinite amount of times from 20, you still do not achieve 0. The answer is not 0, nor is it an infinite number. It is just impossible to achieve 0 via such repeated subtractions, hence 20/0 is undefined. Nevermind this, because as I explained firstly, division is not repeated subtraction. The reason division by 0 is problematic is because, in order for division by a quantity A to be possible, you need to have the following property: if A·x = A·y, then x = y. This does not occur with 0. 0·1 = 0·(1 + 1), but 1 = 1 + 1 is false, in general. So division by 0 is hopeless.
@@angelmendez-rivera351 I think you missed the point of glorified subtraction but that idea does work, 28 divided by 4 is just 28 minus 4 over and over till its 0, which is when it's been subracted 7 times
@@thefloormat3297 No, dude, I literally addressed it within my first sentence. Maybe you do not know how to read. Also, I already explained how subtraction does not work. You cannot subtract 0 over and over from 20 until you get 0. It is impossible.
6:14 the answer for the calculator is defined by IEEE floating point standards and generally requires that software implement exception handling such that when the processors encounters a divide instruction with a zero operand it generates the divided-by-zero exception so the software can decide what to do.
0/0=0 and 1/0= 10^infinite 0. If you want me to explain i am more than happy to. Another theory is that anything divided by 0 actually equals itself. ( 1/0=1 )
If I understand my computer science right, computers' physical arithmetic processing units throw errors when they're ordered to divide by zero, which would cause horrible breakage. In practice, though, the command to divide by zero is intercepted by stuff like the operating system long before it actually manages to reach the hardware.
I think James' first description is pretty much perfect. You just keep subtracting a number until you get to zero. If you did 20 - 0 an infinite number of times, you'd still end up with 20, because every step leaves you with 20. So infinity essentially has no effect on subtracting (or dividing by) zero.
So a lot of these arguments are akin to the arguments used against imaginary numbers, basically saying "it doesn't make sense." But, like imaginary numbers, why can't we just say, "okay, sure, they don't make sense," and declare that they exist, just to see where it takes us? We did it with numbers larger than infinity (see that long and mindnumbing VSauce video), so why not with "supernihlic" numbers?
To get 1/0 = 2/0 into 1 = 2, you multiply by 0 on both sides, which we currently say is well defined. To get 1/0 = 2/0 into 1 = 2, you divide by 0 on both sides, which we see we cannot define unless we throw out multiplication by 0. A lot of things seem like nonsense if you don't pay attention in class.
And this is simply because infinity and 0 are both concepts, not numbers. It is present in mathematics because it is quite useful, such as algebra but to an extent. The very first number systems didn't include a zero at all, some argue that this is why the Roman Empire has fallen.
Lots of people do this. You pick up handwriting habits like this so you can more easily distinguish between symbols that look the same. x and the symbol for cross products, for example, look similar and will confuse people unless you draw the letter x as half circles.
This is a relatively common convention tbh. It was specifically adopted so that 'x' would be more readily distinguishable from the multiplication symbol in mathematical proofs and textbooks. A common alternative was to use * as the multiplication symbol, as most scientific calculators do.
I recently learned what the actual name for 0/0 is in Calculus. It's called an indeterminant, because it can give any answer. If we want to solve it, we need to know the function that created the 0/0, as they show. Then we take the derivative of the top and the bottom (separately), and try to divide again. We repeat until we don't get a 0/0
That’s not quite accurate. An indeterminate form like 0/0 is entirely meaningless on its own and fundamentally can not be “solved” unless you’re talking about in terms of a limit. Furthermore, 0/0 isn’t the only such form, so your use of L’hopital often isn’t applicable.
@@cpotisch Fair enough. Most of the time, the indeterminate form can be converted into a form usable with L'H. Although, you can just use the fact that e^x grows faster than x to get a quick answer
Oh c'mon, it's usually the otherway round. Unlike mathematicians, engineers are too boarged down with deadlines and budget constraints that they hardly have any luxury to play with theories and concept. Otherwise the boss would show them the door 😅
Usually the way I explain it to people is that almost the entirety of calculus is an attempt to simulate dividing by zero. There's that entire branch of mathematics (which most people find too complicated to be worth learning) that is pretty much just answering this question, and it's still a fuzzy and imperfect answer. So if you wanna see why you can't divide by zero, a basic overview of calculus often will do the job if it's being explained well.
Also, dividing by zero doesn't work because 1 would then equal 2 lets say this: a = b a^2 = ab a^2 - b^2 = ab - b^2 (a-b)(a+b) = (a - b)(b) and here, you would say that you could divide by (a - b), and if we do a + b = b b + b = b 2b = b 2 = 1 the problem is dividing by (a-b) which in this case is zero
I still remember that day when I was in the middle school. Our math teacher, let us use 1 divide some positive numbers smaller and smaller, than we found the results bigger and bigger. Then we use negative numbers bigger and bigger, and the results were smaller and smaller. On that day all of us remembered we cannot use some numbers simply to divide 0.
+Marcus Johnson - You sound like a guy back in the 17th Century, "0 is nothing"??????????? Just...wow... I laughed quite a lot when i read that... You made my day XD
The way I see dividing by 0 being nonsensical, is thinking of division as reversed multiplication (which it is): 20/4 assumes there is a number that, when multiplied by 4, equals 20; and there is. It's: 5. Dividing a (non-zero) number by 0 assumes there is a number that, when multiplied by 0, equals that (non-zero) number; which, obviously, isn't true. As for 0^0, it's just (0^1)/0 (since a^0 = (a^1)/a) = 0/0, which could literally be anything, equally likely. The reason, why people say: "a^0 = 1", is, because a^0 = (a^1)/a = a/a, which *_USUALLY_* equals 1; but that reasoning doesn't really work with 0, as discussed earlier.
If anything divided by 0 = 42 and 42 is the answer to the ultimate question, then anything divided by 0 (x\0) IS the ultimate question. That means that the answer to x\0 is the meaning of life and everything else. Come to think of it, lim x->0 = infinity (positive or negative) but never reaches 0 itself - it's composed of everything in the universe except for a point where there is nothing. Oh man, I don't know, if you catch my drift. I'll call it Caldoon-Adams-Julekmeister's Law of Relative Existence :)
@@areadenial2343 but zero is defined, its when there is nothing. But infinity is undefined, because no value can represent it. "Oh, the biggest number is 10^99999", "well, what if i add +1?".
@@Ph0n3numb3r You're half right... no *finite* value can represent it. Because you can't represent an infinite value with something finite, who would have thought? Really, infinity is the opposite of zero. Zero represents nothingness, a lack of value. Infinity represents eternity, a never ending value. So, a 1 followed by a never ending trail of zeroes. It just keeps going, forever.
Here's another way of presenting N / 0 = 0 (written in Lua syntax): N = -1 C = 0 while C > N do N = C R = A - B C = C + (A > R and A >= B) A = A - B end
"\" will be square root. 2\-1 doesnt work (2 numbers the same, multiplied together are always positive: -1*-1=1 but 3\-1=-1. if the "n" is odd it will be -1. if its even, it equals nothing (exept perhaps 0^0)
Negative infinity plus positive infinity is zero. The graph made perfect sense. They are symmetric mirrors of each other and cancel out. both exist at once to make the curves cancel.
If negative infinity plus positive infinity would always equal zero, the following would hold: (+inf) + (-inf) = 0 lim(x) + lim(-2x) = 0 lim(x-2x) = 0 -inf = 0 You get different results depending on what you put in. That's why you say it is undefined.
A long time ago Mr. Talbot, my maths teacher, said that we can't accept dividing by zero because if we do we can 'prove' false things. I can't remember exactly how he did it but he proved that 1 = 0. He then said that if you can 'prove' one false thing you can 'prove' any thing that is in fact false. A quick google found this; x and y are 2 non-zero numbers where x=y. So x^2 = xy. Subtract y^2 from both sides, X^2 - y^2 = xy - y^2. Divide both sides by x-y we get x + y = y which is clearly false. Dividing by x-y when x=y is dividing by zero. which is why this goes wrong.
Donald Knuth disagrees about 0° bring undefined. He talks about that in a very interesting article named "Two Notes on Notation". I recommend reading it, it has convinced me that 0°=1 is the best choice. I agree with him and I point out that arguments about limits have at least 3 problems. 1. An operation is nothing but a function and a function has no obligation to be continuous so the possible value of any limits with (x, y) going to (0,0) don't need to have any relation with the value of such operations at (0,0). 2. Operations, like any function, don't have the obligation of being continuous. Add to this the previous point. 3. Before you prove anything in mathematics you must first have clear definitions (or axioms) of everything you are dealing with. So in order to prove anything (like limit values or inexistence of limits) about the cited operations you must FIRST define them entirely and that means also define their domains and values at any point, including possibly (0,0). So formally speaking you must decide about 0° (and all x^y values) BEFORE saying anything about limits involving x^y. That said, since 0 is a natural number, we should define operations involving natural x and 0 in the context of natural numbers before passing to limits. And in the particular case of 0° there are many uses of the identity 0°=1 in discrete contexts and that makes many people decide for adopting it.
0:16 ⛔ Division by 0 and 0^0 are problematic. 0:31 🔍 Why division by 0 isn't simply infinity. 2:00 🛑 1/0 ≠ infinity; it leads to mathematical contradictions. 2:56 📈 Limits don't make 1/0 equal infinity; they differ from different directions. 5:43 ↔ Approaching 0 from different sides leads to different results (±infinity). 5:59 🖩 Devices can't handle 1/0; it's an unresolved calculation. 6:45 🧮 0^0 is contentious; arguments for both 0 and 1, but undefined due to limits. 10:21 ❓ Undefined result for 0/0 depends on the approach angle.
"You"? Which "you"? There's 2 people we see in the video, which one are you talking about? ...Or do you mean the plural "you" and combined both of them?
Jay Jeckel Come to think of it I think he does it on purpose. Because in the end it serves the same purpose and it's just a formality, he probably does it for fun to get under his mathematician friends skin.
Ivo Wilson I always assumed it was because he is from the UK and they do some things weird over there, like calling math 'maths' and sports 'sport'. Could be easier drawing on a chalk board or what you said. Either way, he does some great videos and his channel is worth checking out if you haven't already.
Well, I understood most things, but I think you need more than basic logic to understand the bit about the imaginary number axis and graphing the crazy squiggly lines because of it.
What I find a more intuitive explanation for why 0^0 is impossible is this: This video mentions multiplication is glorified addition, well exponentiation is the next step of that, glorified multiplication. As the exponent gets lower and lower you multiply less and less. 5^3 = 5*5*5 5^2 = 5*5 5^1 = 5 Now what happens when your exponent goes below 1? You start doing the opposite of multiplication, division. 5^0 = 5/5 5^(-1) = 5/5/5 5^(-2) = 5/5/5/5 This is why x^0 is always 1, because you end up calculating x/x. But now we replace x with 0. 0^0 = 0/0 By doing 0^0 you end up dividing 0 by 0, which this video explains, is impossible.
I'm amazed that there are still people being recommended this video and commenting even today, and here's you providing actual insightful knowledge on the topic at hand. Although I guess maths is kind of a timeless subject. ...unless time is one of the axes on your graph...
This is a nice (and pretty common) argument about 0^0 being undefined, but it actually doesn't work. The connection that x^0 = x/x only works when x is nonzero. Like, the way you show that x^0 = x/x is valid when x isn't 0, but is invalid when x = 0. This means you can't plug in x = 0 later. One thing to keep in mind is that the exponential rules you learned in school work very well if you're dealing with _positive_ bases, but they can break down when your bases is nonpositive (negative or 0). As an example, most people learn the rule that (a^b)^c = a^(bc). And this completely works if a is positive, but can fail when a is negative. In particular, take a = −1, b = 2, and c = 1/2. On one hand, (a^b)^c = ((−1)^2)^(1/2) = 1^(1/2) = 1. On the other hand, a^(bc) = (−1)^(2*1/2) = (−1)^1 = −1. So exponential rules may not work when the base isn't positive. Then general rule that your argument relies on is that x^(a−b) = x^a/x^b. This rule actually holds pretty well for most numbers, but it does not hold when x = 0 _at all,_ regardless of the values of a and b. If this rule were valid for x = 0, we could also say, for instance, 0^2 = 0^(4−2) = 0^4/0^2 = 0/0, which is impossible. We would then conclude that 0^2 is undefined. Of course, 0^2 is very well-defined and has a universally agreed upon value of 0. So this argument can't be right. And you can go through the steps of this argument. The only thing that isn't absolutely solid is moving from 0^(4−2) to 0^4/0^2. 0^0 is a bit of a pet peeve of mine because tons and _tons_ of mathematicians agree that 0^0 = 1 is the best way to handle the situation. If you're working in a "discrete" branch of mathematics (one that doesn't focus on continuity), then 0^0 = 1 will _always_ work in _every_ formula where it arises. You only get into trouble with 0^0 when you confuse limiting forms with arithmetic and assume all functions must be continuous on their domains (which is false). Yet there are still many _mathematicians_ who perpetuate bad arguments about 0^0 and argue that is has to be undefined, despite (discrete) mathematicians' knowledge otherwise. (This is not an attack on _you._ It's an attack on people who _should_ know better because they have been exposed to this way of thinking already.)
A number divided by zero lacks an equation. The person asking "What does 5 ÷ 0 = ?" Is like him asking, "What does 5"? See? When zero follows the division symbol then no equation takes place. We've left the realm of mathematics and returned back to language. I'm surprised that I've never seen this explanation offered before. It is however the only one that explains the question. When we attempt to divide by 0 we're no longer dividing. Its like any attempt to divide with zero automatically erases the whole procedure.
This is true for processors and the DIV instruction, when you try to divide by 0 there it fires an interrupt that basically means "Result is undefined". (It basically checks if there's a 0 anywhere in the 'equation', and if there is, it doesn't calculate anything) I'm not sure if that's true for all processors, but the ones I have experience with use the interrupt method.
I find I don't understand what you're saying here, which concerns me as you say that it's the only phrasing that successfully answers the question. How is it that you're able to say that "divided by zero equals" is equivalent to saying nothing at all? If math has proven capable of making proper use out of numbers that don't even exist (square root of negative one, an imaginary number), then why does this simple utterance disappear when nothing else does?
When he said, "For all we know, this line may wrap around the entire universe and connect" (paraphrased a bit), that got me thinking. It can't, and here's why. What mathematicians do to prove certain postulates or theorems occasionally is that they assume the end as an axiom, so let's assume that the number line does, indeed, wrap around the universe and connect end to end. Well, we also assume by this and the limit equation at about 5:00 that infinity is on one end and negative infinity is on the other. If this line wraps all the way around, end to end, and treating the respective infinities as the points on the line where it terminates, this would mean that infinity and negative infinity are adjacent to each other on this line. Not only are they adjacent, but there are also no numbers between them. There is no value that is greater than infinity (because x + infinity = infinity, whereas x = all real number) and no value is less than negative infinity (because negative infinity - x = negative infinity, whereas x = all real numbers). Because there is no value greater than infinity, it can't be possible to count up from infinity to negative infinity. And you can't count down to get to positive infinity. Another issue would be that the function 1/x approaches positive infinity from the right and negative infinity from the left. This sentence treats infinity as a location, not a number, just as they say in the video. Infinity is not a number and cannot be treated as such. But saying that it is at the end of the number line and connects both sides means that there is a terminal location for infinity, which there isn't. (Terminal meaning simultaneously that there is a singular value that we can point to and say that is this number and that it is at the end of the line.) Infinity has no conclusive end to it because there are many ways to represent infinity, such as: 1+2+3+4+5+6....ad infinitum *also* 2+4+6+8+10+12....ad infinitum *therefore* 1+2+3+4+5+6....ad infinitum = 2+4+6+8+10+12....ad infinitum Both of these number sets add to infinity. But one number set is clearly twice as large. If you wish to simplify it, this can also be represented by infinity = 2 x infinity. How can a number, cardinal or ordinal, be multiplied by any number other than 1 and still be equal to itself? Short answer, it can't. Long answer, it caaaaaaaaaaaaaaaaaaaaaaaaaaaan't. *In conclusion* There is no way to mathematically represent the fact that the number line wraps around. These problems have to be addressed for that to be true, and so far that's not possible, if it ever could be. Also, due to the number line wrapping around, it would also be true that negative infinity and infinity are equal, but I don't know how to prove that. I just intuitively know it. Thank you for coming to my TedTalk.
Doesn’t the real number line pretty much wrap around in a real-number cross-section of the Riemann Sphere? Also, 0 can be multiplied by any number and still equal itself. In fact, it can’t be otherwise. Or are you saying that 0 is not a cardinal or ordinal number?
@@paulchapman8023 I don't know anything about the Reimann Sphere, so I can't argue it's importance (though that doesn't mean it has none). As for zero, I genuinely hadn't considered it, despite the fact that it is cardinal and ordinal. It feels like a cop out of an answer to call it a special case, but i can't think of it any other way. Given its other exceptions (can't divide by it, exponential is 1 always, etc), I don't think its unfair to label it special and consider it separately in some other proof. That was a great question, for a long ago i made this comment I still can tell I hadn't considered zero at all, thank you for bringing it up!
I did not say that infinity is any number.I said 0x(infinity) is an undefined number so you dont know whether it is equal to 1 or not , therefore you can not say that 0x(infinity)=1 is an impossible equation, it is an undefined equation. And you can do operations on infinity. For example: (1/infinity)=0 and: (+infinity)(-infinity)=-infinity
I always hated math and no one I know likes it, but it is nice to see people with a real passion and love for maths/numbers to make it more interesting
A CPU will actually stop the running program immediately when encountering a DIV0 and throw what‘s called an exception. A special part of the operating system will then take over and handle the exception, e.g. showing a blue screen.
If you look at zero in terms of inversion, zero is essentially "neutral infinity", in a way. If you take the inversion of zero with any base radius, you will get a variation of infinity as the answer.
I think you're confused in that you are making weird calculations based on our imperfect, artificially created interpretation of mathematics. Doing a bunch of maneuvers isn't proof that nothing is equal to everything, it's just a flaw in the math we created.
_This Comment is cross-posted!_ 1 is a more consistent answer. The *Taylor expansion* for e⁰ will be *0⁰/0! + 0¹/1! + 0²/2! + 0³/3! + ... = e⁰ = 1.* The only term that is not 0 is *0⁰/0!.* There is also the *Taylor expansion* for *cosine.* If *n* objects each have *k* states, then the equation for the number of the set's positions is *n^k.* Think about the number of positions that [a set of 0 objects each with 0 states] has. This is philosophical, but it is one state. As for *0^x = 0,* that is only true for _positive_ exponents of 0. The Binomial Theorem also relies on the *0⁰ = 1* statement. As for limits, those are only accurate to the true value for continuous functions. Take the piecewise equation *y = x if x ≠ 5, y = 1 if x = 5.* The limit of y as x approaches 5 is 5, but *y = 1* AT *x = 5.* As for the *Product&Quotient Rules* of exponents, under certain circumstances, those are false for 0. I hope this makes sense.
![[#2024MAMA] ROSÉ (로제), Bruno Mars - APT. | Mnet 241122 방송](http://i.ytimg.com/vi/dgGqD28J6aQ/mqdefault.jpg)
Matt is very smart for a guy who writes infinity as double zeroes instead of a laying eight
What if he writes eight the same way?
And X as two C having each other's back
@@marzi_kat It's treason, then.
@@rorschak47
Well that’s cause it’s a cursive x
@JZ's Best Friend They would put him in a room with a quadratic floor and call it the Parker Square.
I suggest we define 1/0 = blue
Jonathan Tanner
Look at me
Jonathan Tanner make a petition
1÷0=blue. The newest axiom in mathematics.
x/0 = blue(x+1)
@@bsm239 1÷0=Blue×1+1=Blue×2=2Blue
"glorified adding" is the best description of multiplying ever
would that mean exponents are extra glorified adding?
@@BasicEndjo glorified multiplication
@@shnob4916 yeah and multiplication is glorified adding. then exponent is *extra* glorified adding
An article in the Onion from 1907 reported that a record breaking number of American children are staying in school beyond third grade. They are learning advanced skills such as multiplication, which we are told, is a powerful form of adding, resulting in numbers so large that three or even sometimes four figures are required to write them.
This is what I told my 2 grader. “Fast addition”
My 7th grade algebra teacher would only whisper of dividing by zero because it would “upset the calculator gods”. He was one of my favorite teachers ever.
Great anecdote
My math teacher said he could taste numbers
@@malteepmeier Ah, Synesthesia!
@@malteepmeier mine snorted cocaine in class and offered some to us.
@@cones914 Disgusting! Where is that teacher located? So I can avoid it
"Only a nerd would tell you differently."
*cuts to Parker* - Sooo, first of all [...]
Even better "... and that's when you cut to Matt telling them differently."
i clicked the [...] in ur comment wtf wrong with me lol
"And then we cut to a nerd telling you differently."
exploshi I clicked the [...] on yours😂
thatsthejoke.jpg
1÷0= infinity
2÷0= Double infinity
There I Fixed it
@Interesting Numbers Wait a minute, then you can multiply both sides by 0 and get 1=2. I think the Illuminati must be at work here. -lol
@@coulombicdistortion1814 Here's the thing about multiplying by zero: anything multiplied by zero is zero. So 0(1/0=2/0)
(1*0)/(0*0)=(2*0)/(0*0)
0/0=0/0
Travis Ryno I have been stuck on this since last evening. My 13 yr old told me exactly this, and then used Banach-Tarski model to say that 1+1=1 is mathematically possible. I don’t know right now whether to believe his hypothesis or continue to say x/0 is undefined.
@@annoyinglyfast5972 He is saying that the logic is wrong
@Travis Ryno therefore 0/0=0
1/0 = blue the secret is out
Lol.
Oh deah, it's a poblem
He used a 1/0 Sharpie.
Shhh, You're not supposed to tell anybody
Are you talking to Blue the Dog about the secret?
A video featuring both Matt and James is such a lovely treat. They are infinitely different.
i see what you did there hahah
Gosh you can’t say that
For the "why does it return Error in a computer" question, the division assembly instructions (at least for x86) are designed to generate an interrupt when the divisor is zero. In other words, they are told to error out.
What would happen if they werent?
@@Xnoob545 Presumably it would attempt that forever. It'd never find its result, and the part that tells it to stop has been chopped off, so it'll just never stop
@@Xnoob545 setcomputeronfire.exe would initiate and well... You get the idea.
@@y-ax2-bx-c5 its like a minecraft world made out of sand
Just falls fprever amd uses exponentaially more power
@@Xnoob545 cpu would hang at 100% usage trying to compute the result of what cant be computed, until you restarted it. therefore safety instruction/lock was added to prevent such.
"BUT, if I am naughty..." Oh baby, talk nerdy to me~
LOL
+James Lynn Savage
+James Lynn
Rounding to the first decimal place also counts as naughty. Computing ∫e^x dx makes one horny.
+James Lynn oh my lord
pearl you're smart, what's the real answer here to 1/0
3:05 Noooooooooo!!!
Draw infinity as a continuous loop not two circles!!!
It's ugly
@Al Gee Writing it as a continuous loop has a more comfortable flow than two separate circles
two circles are not a lemniscate!
Yeah, the entire point of the symbol is being a literal neverending loop
haha infinity go oo
Now, I had always been taught that X/0 was "undefined", while 0/0 was "indeterminate". The logic behind this is that the denominator (or "divisor") should always be able to be made equal to the numerator, by multiplication with some factor.
So, for example, 1/2 = .5, thus 2 can be made equal to 1 by multiplication with.5. However, in the case of X/0, there is no factor that can make 0 = X, since 0 times ANYthing is always 0. So, there is no correct answer, therefore, the problem is "undefned".
On the other hand, in the case of 0/0, literally ANY factor will make 0 equal to itself, so there is no INcorrect answer. Thus, in essence, any value is equal to any OTHER value, which is impossible. Therefore, the problem is called "indeterminate", since one cannot determine what value best solves the problem.
@Vikas Bhardwaj what if we define 0/0 as equal to 0
I know you said this is what you were taught, but it bears mentioning that this is just incorrect. There is no such a thing as "indeterminate" in mathematics, and people need to stop using this word forever. 0/0 does not exist. Period. That is all there is to it. And there is a very simple reason it does not, but it just has to do with what division itself is. Division is just multiplication: multiplication by the reciprocal, to be exact. 0 has no reciprocal. So one cannot divide by 0.
@@angelmendez-rivera351 because in calculus, 0 is not exactly 0, 0 can be 0.0002 or -0.00001, numbers are not exactly their values. That’s why there is indeterminate
@deaf I fail to see how those points connect. 0*x = 0 for all values of x is a true statement. I don't see how this implies that 0/0 = 1 any more than it does any arbitrary number.
@@angelmendez-rivera351 Yes, in terms of numerical value, indeterminate forms are considered undefined. But they are very useful in calculus because of how they affect limits. (f(x+h) - f(x))/h = 0/0 when h=0, so it's undefined. But the limit as h approaches 0 is very much defined (when f(x) is continuous), and is in fact the definition of the derivative. If 0/0 is just undefined, derivatives don't exist, and calculus doesn't work. That's why we have indeterminate forms, at least when working with limits
An accountant, an engineer, and a mathematician are asked how much is 1 + 1:
Mathematician: "1 + 1 is 2 and I can prove it"
Engineer: "Well, 1 + 1 is anything between 1.8 & 2.1"
Accountant: "It depends. How much do you want 1 + 1 to equal?"
Democrat: 1 x 0 = transgender
Republican: 1 + 1 = homophobe
Quantum physicist: i don't know until i actually calculate it
Surrealist: yes
Communist: 1/2 for me, 1/2 for you, and 1 whole for the state
It depends whether we sell or buy.
How to make a million dollours on paper with 50
Numberphile: Imma head out
12:49 "we could make it anything we want it to be depending on the angle we come at it from"
sound life advice right there
When i was a child. I thought 0 and -0 were different numbers, and i kept counting wrong when going from positive to negative or negative to positive
In IEEE 754 format they *are* different numbers. They behave very much alike, though.
What's bigger, zero minus zero, or zero minus negative zero? Lol just kidding.
@@p.as.in.pterodactyl1024 Who is bigger, Mr. Bigger or Mr. Bigger's baby? The baby, because he's a little bigger.
Original commenter: You were born with what is called "Ones' complement"! I guess you were upgraded to "Twos' complement" since then.
@@ΝίκοςΙστοσελίδα What is that?
There's a video around of an old mechanical calculator which gets stuck in a loop when trying to divide by zero, and the operator has to press the abort button to stop it running.
Nothing bad happens - it just keeps subtracting zero and counting how many times it subtracts zero and it never finishes.
Most CPU's have a specific return code for "Divide by Zero Error", meaning it doesn't attempt to calculate as the error is handled at the CPU level.
Number_055 return 0;
I think it's implemented at OS level. And older operating system just tried to subtract 0 from the number forever, forcing you to turn off the power and turn it on again.
@@DanCojocaru2000 If you actually think that applications call the OS to perform calculations then you haven't got a clue what an operating system actually does and doesn't do. Division is not a system task, it can be performed by any application that is directly using the processor (CPU) at user level. Actually, most CPU's have division build right into them...sometimes incorrectly, check the Pentium bug (for floating point division).
Specifically, it's a hardware trap (ie. hardware exception) generated by the CPU at the time of division, at least on x86 / x86-64.
Edit: I made a mistake in my original post, and I apologize. A divide-by-zero will return a "not a number" (NaN) result for a floating-point division. I don't know off the top of my head what result an integer division returns - this is something I should either look up or simply test - but the divide-by-zero register is still set, which can be queried to determine if an exception should be thrown. Floating point values may contain infinity and negative infinity as actual values, and if you want, you can treat a divide-by-zero as infinity, and I have in fact seen API's that do this, but generally speaking, you don't want a divide-by-zero to ever be a valid operation.
Original post:
@@majormalfunction0071 Intel CPU's will happily divide by zero and return either infinity or negative infinity, depending on the sign of the operation - they also differentiate between zero and negative zero; the sign is simply a bit in the return value. They will, however, as Number_055 noted, also set a "divide by zero" register notifying the application requesting the operation that a division by zero occurred, which the application may then treat any way it likes, including treating the operation as an exception and possibly crashing itself. I wholly agree that "infinity" is not a valid return value for a divide-by-zero, but the IEEE standards committee had to settle on something that would work from a technical standpoint.
The way he smiles when he brings in the complex numbers...
And that all the while glossing over X^X for negative X looking really strange (it's jumping all over the complex plane and is basically discontinous everywhere). That is not a function for which you want to find a limit. The complex version must be just as bizarre.
Don’t expose them to sunlight, don’t let them eat after midnight, don’t get them wet, and never divide by zero
I understood that reference!
But it’s always after midnight...
Do not touch the operational end of The Device. Do not submerge The Device in liquid, even partially. Most importantly, under no circumstances should you divide The Device by zero.
AND NEVER EAT PEARS!
… And those are the rules for math gremlins.
There's some great footage on RUclips of mechanical calculators, oldschool ones, dividing by zero. No programmed-in "Math Error" there, the things just spin forever making a racket, they're probably subtracting zero over and over but maybe some of them are failing in a more clever way.
Error; task completed successfully 😂
Plot twist; the entire Numberphile series is a promotion for Sharpie.
vihart???
Andrew Jones - And brown paper.
I can smell the sharpies.
And the brown paper
DUN DUN DUN
÷0 looks like a screaming person
Yep
Fitting
It's screaming at you for trying to destroy the universe.
Thats the reason you cant devide by zero.
But you can devide zero.
Or like a key
7:44
"We're gonna slide it in and, in fact, we're gonna have to do it from both directions"
O___0
Liam Dienemann
“more than a numberphile”
An Infinityphile XDXDXDXD
There's a reason why infinity is drawn as two circles.
Nice
"Divide"
-No
"GlOriFieD SuBsTrAcTioN"
- *YES*
Substraction?
That is like roblox ad...
Thank me for i was the 69th to like
Jk
@@niccolopaganini1782 hello paganini
0/0 = calculus
I love these numberphile videos because you can litterally notice how they get high on math as the video goes 😂
i see much enthusiasm :D I suggest "a hole in a hole in a hole" :D
Math makes me horny
It's the only way to fly.
That's what happens when you inhale sharpies.
*Meth
"The problem is it's a dangerous number and a lot of things can go horribly wrong with 0"
"Mom I got 0 in maths"
*UH OH*
Lol
if it was art, it would’ve been better
@@boncoderz1430 you mean nice zero?
@@tenplusten1116 Especially if you're from Austria...
@@leyyesuh oh…
6:10 Yes, computers are taught not to divide by 0. The reason is because bitwise math operations are only add and subtract. Multiplication is just repeated adding, while division is repeated subtracting. If you divide by 0, you are telling the computer to subtract 0 from the original until the value of the original is
≤ not
Happy New year sir
But Javascript gives back Infinity..
@@jathebest2835 That doesn't matter since the sign of the quotient is determined by the dividend. So are you going to get it as infinity or negative infinity? Since the answer is undefined anyways, is there a point in computing it?
@@mdsharfuddinmd5710 hi you too
Multiplication and division are the next iteration of addition and subtraction. The iterations beyond those are exponents and roots. When you get beyond that, it gets really hairy. Layered exponents (also known as "towers") and roots (just the reciprocal of towers) are as far as most people dare to go. But you can technically go as far as you want, and Knuth invented a special notation to explain the weird realm beyond layered exponents/roots. It was used to create one of the largest numbers ever conceived, Graham's number.
2:20 - 2:30 But 1/0 is equal to blue.
When you asked the old Sinclair calculator from the 70s to divide by zero, it actually tried! It would give you multiple answers one after the other until eventually it spat the dummy, showed all the decimal points and locked the screen.
spat the dummy? that isn't a phrase
Ben P it is in Straya
I consider 0/0 to be a feature, not a bug.
Simple Algebraic Rearrangement tells us:
If Anything * 0 = 0,
Then 0 / 0 = Anything.
Intuitively, 0 / 0 represents the question "what number can you multiply by 0 to get 0", to which the answer is clearly "Anything".
If 0/0=1 and 0/0=2 then 1=2 by the transitive property. If you allow that, the you can say that every number is equal to each other.
The transitive property doesn't always work that way.
√1 = 1 and √1 = -1, but 1 ≠ -1
MumboJ the square root symbol like that that is a function. when you use the square root symbol like that you are taking the principle root which is always positive. You mean to right x^2=1 which has to possible solutions that make that statement true. If you want the negative value you have to put the negative sign in front.
Which is exactly how 0/0 works.
It is a rearrangement of 0x=0, to which anything is a solution.
Function Symbols are often used to represent this concept, and the phrasing I used was not incorrect.
MumboJ a square root of a number can be either positive or negative. Its because both positive squared and negative squared are positive. Example: √1=±1
√4=±2
√2≈±1.414
A decade later and still a fantastic video!
Ten, meaning one, zero. Coincidence? I think not!
0 is my favorite number because it has no value, just like me.
I read this and I laughed. Thank you very much for that laugh.
:)
ᎢᎻᎬᎠᎾᎠᎾ ᎬNᎢᎻᏌᏚᏆᎪᏚᎢ jokes on you, our numbers don't work without a concept of zero
ᎢᎻᎬᎠᎾᎠᎾ ᎬNᎢᎻᏌᏚᏆᎪᏚᎢ CRAWLING IN MY CRAWL
Bad day?
Ooh ..hope that was limited to being a joke.
*Santa:* You don't get presents this year because you were naughty
*Mathematician:* What! Why?
*Santa:* You used infinity as an answer
in high school I was doing a problem on the blackboard in an algebra class and I was finishing it fast so I was writing both sides of the equation (my way of doing it) and the teacher saw it and yelled "algebraic sacrilege!!!!" and that scared me lol and everyone else in the classroom. I swear that we almost hear thunders falling on us. Sufficient to say that I never had the opportunity to explain to him that I was still writing my answer, so I just completed the answer as a "correction".
@@marilynman You're supposed to write both sides?
@@circuit10 I meant that when you start writing it, you begin with the right side, you finish writing that side and then move on to the right side. I was doing both sides at the same time.
X/0 = santa
@Eero Naughty boy. Now you cannot wish to Santa anymore. Even finding out the meaning of life and solutions to infinity.
"We have to slide it in, from both directions." - Phwoar........
stop. lets keep it PG
+Sarah Cartwright Hi Sarah!
+John Yyc zero ain't PG mate. Zero is a dirty boy.
+Sarah Cartwright "So you say, 'Well, if it doesn't matter which side we're coming in from... surely we can just call it one.'"
+John Yyc Even PG movies are allowed brief adult moments.
11:23 Even the painting is interested in mathematics.
lOL
For some reason, the way Matt writes his "x" is deeply unsettling to me.
Shouldn't be allowed to work as a mathematician if you write x like he does LOL
How else would you do it? Like a normal written x?
@@clarkeysam yes, you cross two lines like a respectable human being.
Tauno Kekkonen no, that x is anti calculus.
You want a nice, curvy and sexy x.
He writes it just like how you learn to write your x in cursive in second grade
I divided 1/0 in my calculator and now it runs Super Mario 64.
if I divide by 0 on my smartphone, can my smartphone calculate a rocket launch?
@@farisakmal2722 Probably
I divided zero on my table and now it can shoot lasers and fly
ok............
I inputted 1/0 into a sideways 8 and now every time I draw an 8, it Runs fortnite
The computer is actually taught to not divide by zero. There are many situations in software where dividing by zero is caught and protected against. My brother used to work in a hardware store and he had a computer that gave a 'divided by 0' blue screen. According to the story, he laughed insanely laud at that blue screen. Usually that doesn't happen but the computer had a defect RAM which fed corrupted data into the processor as it fetched the information to execute the micro programs. The processor actually had a build in protection to prevent dividing by zero, it stopped the operation and 'breached' away from its micro instruction to the error handling of windows which on its term showed the blue screen.
In short, the computer doesn't even attempt to divide by zero. If you were to try and do it it would probably try to apply a form of implemented long devision which would obviously fail and I have no clue what it would return.
Robert sorry RUclips isn't letting me post my own comments one thing I would note for the people at number phile is it's as easy as defining 0*y=0 y in the complex plane but not =0 so 0 divided by 0 makes no sense since you can turn it into y*0/y1*0 the 0's can be seen to cancel and then you get y/y1 for any values y,y1 and therefore can take on any of any infinite values.
***** Actually, I think that algorithm doesn't quite simulate a division by zero because, for any value you insert as a divisor (if you swapped "int(n) - 0" for ,say, "int(n) - 3", for example), you'd still have an infinite loop (because the condition for the while loop will always be true and there is no condition for it to actually stop).
A true general algorithm for a division of integers would be something like that:
-----------------------------------------------------------------------------------------------
n = int(raw_input("Insert the dividend: "))
m = int(raw_input("Insert the divisor: "))
c = 0
result = n
while True:
result -= m
if result < 0:
remainder = result + m
break
c += 1
print c
print "%d/%d = %d with a remainder of %d"%(n,m,c,remainder)
--------------------------------------------------------------------------------------------------
If you insert 0 as the divisor, the "c" values will explode into infinity on the screen until you hit that close button, however, inserting other positive integer values would return normal division results. :D
(also written in Python, because screw it, i'm on that lazy train too \o/)
Robert
Dividng is reverse of multiplyin so:
4/3 is
4 * (1/3)
and a proof of this is that:
(4/3) * 3 = 4
(a/b) * b = a
so:
if b = 0 and a is any N then a =/= a which as answer is not in set N because any a in this set is equal to itself
(4/0) * 0 = 0 ==> 4=0
The result of this nonsene came from the set. Any result on the corpus of N must result in the corpus of N and 0 is not in even in the set of N.
Szloma Josif Point being?
Robert Fennis
Set dosent include result.
Need a larger set with algebra over biger corpus with a diferent ring and more dimensions.
And of course problem is solved, directX is working perfectly without gimbal lock on this wee issue of dividing by zero.
6:25 totally agree with that. I know that when I do a really intense calculation on Desmos, the calculator displays to me a message saying "definitions are nested too deeply"
I met this channel a while ago, when i was in highschool and used to watch every video. Now, as i'm graduating in mathematics i come back and rewatch the same videos, but now in a different perspective. Numberphile was one of the main reasons i decided to study math in college, despite all flaws.
From the software engineering perspective I'd say that I highly doubt that any commonly used calculator uses iterative process to get an answer for X/0. It's just a check in the code: if operation is division and second argument is 0 then print "Error". So, the first guess is much closer to reality
Definitely more likely. Calculators only really do addition and subtraction so if you tried to divide by zero it would keep subtracting by zero an infinite amount of times, just like they demonstrated in the video. Its gotta be programmed to check for a non zero number to keep it from entering an infinite loop, that seems like the best solution
This is how most applications work, most of the time its baked into the compiler (Roslyn)
It's normally an exception, stopping your execution. If you have a divide by zero in your equation and you don't stop, you're in la-la land. CPUs handle integer division (which give division by zero and overflow), languages have standard libraries for floating point. The standard is to have zero, NaN (Not a number), Inf, and -Inf as distinct results. Most calculators now have this as well (processors are very cheap).
NaN is different than infinity. Infinity normally means it encountered a number which exceeded the maximum value (e.g. 300 factorial), and infinity times zero is zero. Any math operation using NaN gives you NaN as a result. You also can have exceptions for overflow/infinity, and there may be cases where you want to know when you underflow (if you have x and y, which are not zero, but you get zero because the number is too small.. that's not normally one you worry about).
A difficult problem in programming is when you have a one-off problem, where it goes into la-la land, and takes a few steps before it dies. Math is one of those things.
Unless someone forgets to tell the computer not to attempt the subtraction, in which case the computer may crash, which happened to an American warship, computers down for a day
Happy New year sir
Here's a simpler explanation of why n/0 is impossible and 0/0 is undefined. I use it in my 6th grade classes in Italy using numbers instead of letters.
1) division is the inverse operation of multiplication. Calculating a/b means finding a number (let's call it "c") that multiplied by b gives a (in other words, c*b=a is basically the same thing as a/b=c, you're just reading it backwards. For example: 6/3=2 and 2*3=6 are basically the same thing, you're just reading it backwards).
2) if b=0, then you get a/0, which is impossible because there's no number that multiplied by 0 gives a. In fact, a/0=c means c*0=a, and there's no number "c" that multiplied by 0 gives a. Since the operation a/0 doesn't have a result, it's impossible.
3) if a=0 and b=0, then you get 0/0, which is undefined because any number multiplied by 0 always gives 0. In fact 0/0=c means c*0=0, which is always true, no matter what number "c" you choose. Since the operation 0/0 doesn't have one single result (it has infinite results), it is undefined.
I hope this can be helpful.
Also, it can’t be infinity, because even if you subtract it an infinite amount of times your still going to have the number you started with.
But all division does is count the subtractions that took place to reach the number. Therefore, it isn't infinity or the number you started with. It's 0.
20 / 4 = 5 (Five Subtractions)
20 - 0 = 20. No subtraction took place.
20 / 0 = 0 (Zero Subtractions)
@@Vespyr_ No, that is horribly incorrect. Firstly, that is not how division actually works: division is not repated subtraction, and multiplication is not repeated addition. Secondly, even if division did work that way, your answer is still wrong, becaue 20/0 would be equal, by your definition, to the number of times you have to subtract 0 from 20 to achieve 0. The problem is that, even if you subtract 0 an infinite amount of times from 20, you still do not achieve 0. The answer is not 0, nor is it an infinite number. It is just impossible to achieve 0 via such repeated subtractions, hence 20/0 is undefined.
Nevermind this, because as I explained firstly, division is not repeated subtraction. The reason division by 0 is problematic is because, in order for division by a quantity A to be possible, you need to have the following property: if A·x = A·y, then x = y. This does not occur with 0. 0·1 = 0·(1 + 1), but 1 = 1 + 1 is false, in general. So division by 0 is hopeless.
The answer is super existence, a level above every number
@@angelmendez-rivera351 I think you missed the point of glorified subtraction but that idea does work, 28 divided by 4 is just 28 minus 4 over and over till its 0, which is when it's been subracted 7 times
@@thefloormat3297 No, dude, I literally addressed it within my first sentence. Maybe you do not know how to read. Also, I already explained how subtraction does not work. You cannot subtract 0 over and over from 20 until you get 0. It is impossible.
6:14 the answer for the calculator is defined by IEEE floating point standards and generally requires that software implement exception handling such that when the processors encounters a divide instruction with a zero operand it generates the divided-by-zero exception so the software can decide what to do.
Joke's on you, I divided by zero and got an answer. I put 1/0 in my calculator, and got "Error". So, 1/0=Error.
Jude Pelaez makes sense lol
basically, you get something, what programmer wrote. And of course he lies.
Jude Pelaez 0 divided by 0=error
Jude Pelaez So 1/0 is the guy from Zelda 2? Brilliant!
Jude Pelaez but what about 0 divided with 'error'?
0/0=0 and 1/0= 10^infinite 0.
If you want me to explain i am more than happy to.
Another theory is that anything divided by 0 actually equals itself. ( 1/0=1 )
If I understand my computer science right, computers' physical arithmetic processing units throw errors when they're ordered to divide by zero, which would cause horrible breakage. In practice, though, the command to divide by zero is intercepted by stuff like the operating system long before it actually manages to reach the hardware.
"Maybe this line goes all the way around and wraps around the entire universe and things come back up here"
I'm having vertigo
Not surprising if you know the history of the projective plane...
@@digitig *flashbacks
I've always interpreted it as being positive and negative infinity and every possible number in-between.
Not sure if that's valid though.
@@StevenAyre1 yes, 1/0 is every number ever to be thought of at the same time...
"We can no more say that 1 divided by 0 is equal to blue"
I lost it
"we can no more say that *than* [that] one divided by zero is equal to blue"
you missed a "than"
@@meta04 ?
"And people will yell at me if i say its infinitely different" i lost it
2:25Mathematicians definition if “naughty” and “evil” - “Ooh, what if I said 1/0 = infinity? Ooooooh”
I think James' first description is pretty much perfect. You just keep subtracting a number until you get to zero. If you did 20 - 0 an infinite number of times, you'd still end up with 20, because every step leaves you with 20. So infinity essentially has no effect on subtracting (or dividing by) zero.
So a lot of these arguments are akin to the arguments used against imaginary numbers, basically saying "it doesn't make sense." But, like imaginary numbers, why can't we just say, "okay, sure, they don't make sense," and declare that they exist, just to see where it takes us? We did it with numbers larger than infinity (see that long and mindnumbing VSauce video), so why not with "supernihlic" numbers?
1 / 0 = infinity
2 / 0 = infinity
1 = 2
Nonsense, right?
1 * 0 = 0
2 * 0 = 0
1 = 2
Yep. Nonsense.
To get 1/0 = 2/0 into 1 = 2, you multiply by 0 on both sides, which we currently say is well defined. To get 1/0 = 2/0 into 1 = 2, you divide by 0 on both sides, which we see we cannot define unless we throw out multiplication by 0. A lot of things seem like nonsense if you don't pay attention in class.
***** I agree, ( lim x→|∞| ∀x[∞] →∃x[x/0=|∞|] )
And this is simply because infinity and 0 are both concepts, not numbers. It is present in mathematics because it is quite useful, such as algebra but to an extent. The very first number systems didn't include a zero at all, some argue that this is why the Roman Empire has fallen.
PureAwsomeness thank you, i agree entirely.
I hate when people say that. All numbers are "ideas", and zero and infinity are numbers the same way 3 is a number.
The way he writes Infinite Haunts me 3:07
Drawing X as two half circles?
Classic Parker Square.
Lots of people do this. You pick up handwriting habits like this so you can more easily distinguish between symbols that look the same. x and the symbol for cross products, for example, look similar and will confuse people unless you draw the letter x as half circles.
This is a relatively common convention tbh. It was specifically adopted so that 'x' would be more readily distinguishable from the multiplication symbol in mathematical proofs and textbooks. A common alternative was to use * as the multiplication symbol, as most scientific calculators do.
That looks more like a khi
@@Bignic2008 thats actually pretty cool. Definetivly reasonable. 👍
@@smockboy makes sense and is smart 👍
11:50 I see what you did there, NAUGHTy
Freaky Fred :)))))
Who said that mathematicians can't be naughty?
That is the craziest way to write "x"
I recently learned what the actual name for 0/0 is in Calculus. It's called an indeterminant, because it can give any answer. If we want to solve it, we need to know the function that created the 0/0, as they show. Then we take the derivative of the top and the bottom (separately), and try to divide again. We repeat until we don't get a 0/0
L'Hopital's!
That’s not quite accurate. An indeterminate form like 0/0 is entirely meaningless on its own and fundamentally can not be “solved” unless you’re talking about in terms of a limit.
Furthermore, 0/0 isn’t the only such form, so your use of L’hopital often isn’t applicable.
@@cpotisch All the other indeterminate forms can be turned into a 0/0 or inf/inf form, in which L'H can then be applicable
@@gamerdio2503 e^x-x as x goes to infinity?
@@cpotisch Fair enough. Most of the time, the indeterminate form can be converted into a form usable with L'H. Although, you can just use the fact that e^x grows faster than x to get a quick answer
OH GOD NO... He's gonna divide by zer....................
+Sarge!!! BOOOM
Dewey russian kh/ch -Хх
hey i heard someone divided by zero. is everyone okay?
(Bomb explodes)
⚫️
Mathematician: "you can't divide by zero"
Engineer: "Just watch me!!!"
That must be what Denny Pate, the designer of the FIU bridge did, and then the Boeing engineers that designed the 737MAX followed his lead.
Oh c'mon, it's usually the otherway round. Unlike mathematicians, engineers are too boarged down with deadlines and budget constraints that they hardly have any luxury to play with theories and concept. Otherwise the boss would show them the door 😅
I divided by zero and my calculator transformed into Optimus Prime and rolled out
my calculator prints out the entirety of Romeo & Julie and then splits into several people and performs it.
@@bsm239 XD
So lame
Greetings Mortal So lame
This is my favorite video on this channel. Makes me chuckle every time.
Usually the way I explain it to people is that almost the entirety of calculus is an attempt to simulate dividing by zero. There's that entire branch of mathematics (which most people find too complicated to be worth learning) that is pretty much just answering this question, and it's still a fuzzy and imperfect answer. So if you wanna see why you can't divide by zero, a basic overview of calculus often will do the job if it's being explained well.
But u can
Also, dividing by zero doesn't work because 1 would then equal 2
lets say this:
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a-b)(a+b) = (a - b)(b)
and here, you would say that you could divide by (a - b), and if we do
a + b = b
b + b = b
2b = b
2 = 1
the problem is dividing by (a-b) which in this case is zero
These numberphilr videos with multiple interviewees are among the best!!!
I still remember that day when I was in the middle school. Our math teacher, let us use 1 divide some positive numbers smaller and smaller, than we found the results bigger and bigger. Then we use negative numbers bigger and bigger, and the results were smaller and smaller. On that day all of us remembered we cannot use some numbers simply to divide 0.
im surprised they didn't explode
0^0=Spaghetti
Hm I thought it was banana
+Bearboy03
No, 0^Spaghetti is Banana. You were close, though. :)
+Naveek Darkroom 0^0 = 0
+Marcus Johnson Lol - Unless you are having fun, 0 ^ 0 is not 0 :P it's.............................1
+Marcus Johnson - You sound like a guy back in the 17th Century, "0 is nothing"??????????? Just...wow... I laughed quite a lot when i read that... You made my day XD
He draws graphs with arrows on both sides of the same axis. Would rather divide by 0
Why is this so far down!!! Goddamnit that irritates me
Yeah. Because the graph of rational numbers goes in both directions
@@Dragongaga yeah and that's correct i guess
I don't understand, I draw my graphs like that
yes thats by definition correct where on earth did you. go to school that they didnt teach you that, have you never drawn a graph before?
The way I see dividing by 0 being nonsensical, is thinking of division as reversed multiplication (which it is): 20/4 assumes there is a number that, when multiplied by 4, equals 20; and there is. It's: 5. Dividing a (non-zero) number by 0 assumes there is a number that, when multiplied by 0, equals that (non-zero) number; which, obviously, isn't true.
As for 0^0, it's just (0^1)/0 (since a^0 = (a^1)/a) = 0/0, which could literally be anything, equally likely. The reason, why people say: "a^0 = 1", is, because a^0 = (a^1)/a = a/a, which *_USUALLY_* equals 1; but that reasoning doesn't really work with 0, as discussed earlier.
anything divided by zero = 42
come on people! don't you know your DNA?
You must be descended from the telephone sanitizer;)
so zero = life?
ATBPjako Since 0 can be defined as Nothing or None, 0 = 42 could mean "You have no life"
If anything divided by 0 = 42 and 42 is the answer to the ultimate question, then anything divided by 0 (x\0) IS the ultimate question. That means that the answer to x\0 is the meaning of life and everything else. Come to think of it, lim x->0 = infinity (positive or negative) but never reaches 0 itself - it's composed of everything in the universe except for a point where there is nothing. Oh man, I don't know, if you catch my drift. I'll call it Caldoon-Adams-Julekmeister's Law of Relative Existence :)
Even the number of likes on your post has been divided by zero
I divided by 0 and my paper set on fire
Yea, I tried it on my Samsung 8 and it exploded
BEANS
No that is what 2 beans add 2 beans is
That is actually some beans
Or a really small casserole
Infinity is not a numbah...
It can't be treated like a numbah...
I love that guy 😂😂😂
Infinity is certainly not here but it is certainly over yonder.
In many cases, zero can't be treated like a number either. So should we just say it's not a number and call it a day?
@@areadenial2343 but zero is defined, its when there is nothing. But infinity is undefined, because no value can represent it. "Oh, the biggest number is 10^99999", "well, what if i add +1?".
@@Ph0n3numb3r You're half right... no *finite* value can represent it. Because you can't represent an infinite value with something finite, who would have thought? Really, infinity is the opposite of zero. Zero represents nothingness, a lack of value. Infinity represents eternity, a never ending value. So, a 1 followed by a never ending trail of zeroes. It just keeps going, forever.
*number
Here's another way of presenting N / 0 = 0 (written in Lua syntax):
N = -1
C = 0
while C > N do
N = C
R = A - B
C = C + (A > R and A >= B)
A = A - B
end
Can you talk about rooting negative numbers?
victor sodéus i think they have videos on complex numbers. if not there is a really great 13 part series by another youtuber.
"\" will be square root.
2\-1 doesnt work (2 numbers the same, multiplied together are always positive: -1*-1=1
but 3\-1=-1. if the "n" is odd it will be -1. if its even, it equals nothing (exept perhaps 0^0)
Bacon Grease, i^2= -1 by definition. Creates the Complex Numbers and you can have a square root of a negative number.
no real number squared will be negative. ever. if you square any number, by deffinition it becomes positive. i said real numbers.
Bacon Grease nowhere in your comment did you say real numbers though.
If I had numberphile as my math professor, Vsauce as science, I would top the school.
I don't think Vsauce knows curriculum science. He is only interested in the abstract and ambiguous topics of science.
Negative infinity plus positive infinity is zero. The graph made perfect sense. They are symmetric mirrors of each other and cancel out. both exist at once to make the curves cancel.
If negative infinity plus positive infinity would always equal zero, the following would hold:
(+inf) + (-inf) = 0
lim(x) + lim(-2x) = 0
lim(x-2x) = 0
-inf = 0
You get different results depending on what you put in.
That's why you say it is undefined.
you look at both solutions interacting with each other on graph.
You cannot do arithmetic on infinity, it's not a value
A long time ago Mr. Talbot, my maths teacher, said that we can't accept dividing by zero because if we do we can 'prove' false things. I can't remember exactly how he did it but he proved that 1 = 0. He then said that if you can 'prove' one false thing you can 'prove' any thing that is in fact false.
A quick google found this; x and y are 2 non-zero numbers where x=y. So x^2 = xy. Subtract y^2 from both sides, X^2 - y^2 = xy - y^2. Divide both sides by x-y we get x + y = y which is clearly false. Dividing by x-y when x=y is dividing by zero. which is why this goes wrong.
1/0=Blue... i'm going to write that next time i write a calculator program..
Donald Knuth disagrees about 0° bring undefined. He talks about that in a very interesting article named "Two Notes on Notation". I recommend reading it, it has convinced me that 0°=1 is the best choice.
I agree with him and I point out that arguments about limits have at least 3 problems.
1. An operation is nothing but a function and a function has no obligation to be continuous so the possible value of any limits with (x, y) going to (0,0) don't need to have any relation with the value of such operations at (0,0).
2. Operations, like any function, don't have the obligation of being continuous. Add to this the previous point.
3. Before you prove anything in mathematics you must first have clear definitions (or axioms) of everything you are dealing with. So in order to prove anything (like limit values or inexistence of limits) about the cited operations you must FIRST define them entirely and that means also define their domains and values at any point, including possibly (0,0). So formally speaking you must decide about 0° (and all x^y values) BEFORE saying anything about limits involving x^y.
That said, since 0 is a natural number, we should define operations involving natural x and 0 in the context of natural numbers before passing to limits. And in the particular case of 0° there are many uses of the identity 0°=1 in discrete contexts and that makes many people decide for adopting it.
google says 1/0 is infinity and google is always right also google said 0^0 is 1 soo yah.... (btw 0^0 means zero to the power of zero)
0:16 ⛔ Division by 0 and 0^0 are problematic.
0:31 🔍 Why division by 0 isn't simply infinity.
2:00 🛑 1/0 ≠ infinity; it leads to mathematical contradictions.
2:56 📈 Limits don't make 1/0 equal infinity; they differ from different directions.
5:43 ↔ Approaching 0 from different sides leads to different results (±infinity).
5:59 🖩 Devices can't handle 1/0; it's an unresolved calculation.
6:45 🧮 0^0 is contentious; arguments for both 0 and 1, but undefined due to limits.
10:21 ❓ Undefined result for 0/0 depends on the approach angle.
The way you write the 'X' and the 'Infinity symbol' is so weird!
"You"? Which "you"? There's 2 people we see in the video, which one are you talking about? ...Or do you mean the plural "you" and combined both of them?
Typo No idea, the one who does it wrong.
Jay Jeckel Come to think of it I think he does it on purpose.
Because in the end it serves the same purpose and it's just a formality, he probably does it for fun to get under his mathematician friends skin.
Ivo Wilson I always assumed it was because he is from the UK and they do some things weird over there, like calling math 'maths' and sports 'sport'. Could be easier drawing on a chalk board or what you said. Either way, he does some great videos and his channel is worth checking out if you haven't already.
Jay Jeckel Absolutely, I did check it out and even though I'm not a maths guy I fell in love with it
And I'm here pretending to understand everything that they discuss...
Same
you need advanced mathematics understanding
not really. just logical thinking is enough.
Well, I understood most things, but I think you need more than basic logic to understand the bit about the imaginary number axis and graphing the crazy squiggly lines because of it.
Deschain19
well that is true. I finished high school and still don't really get imaginary numbers
Dividing by zero is such a Parker Square move.
lol, only numberphile fans will get this.
What I find a more intuitive explanation for why 0^0 is impossible is this:
This video mentions multiplication is glorified addition, well exponentiation is the next step of that, glorified multiplication.
As the exponent gets lower and lower you multiply less and less.
5^3 = 5*5*5
5^2 = 5*5
5^1 = 5
Now what happens when your exponent goes below 1? You start doing the opposite of multiplication, division.
5^0 = 5/5
5^(-1) = 5/5/5
5^(-2) = 5/5/5/5
This is why x^0 is always 1, because you end up calculating x/x. But now we replace x with 0.
0^0 = 0/0
By doing 0^0 you end up dividing 0 by 0, which this video explains, is impossible.
I'm amazed that there are still people being recommended this video and commenting even today, and here's you providing actual insightful knowledge on the topic at hand.
Although I guess maths is kind of a timeless subject.
...unless time is one of the axes on your graph...
This is a nice (and pretty common) argument about 0^0 being undefined, but it actually doesn't work.
The connection that x^0 = x/x only works when x is nonzero. Like, the way you show that x^0 = x/x is valid when x isn't 0, but is invalid when x = 0. This means you can't plug in x = 0 later.
One thing to keep in mind is that the exponential rules you learned in school work very well if you're dealing with _positive_ bases, but they can break down when your bases is nonpositive (negative or 0). As an example, most people learn the rule that (a^b)^c = a^(bc). And this completely works if a is positive, but can fail when a is negative. In particular, take a = −1, b = 2, and c = 1/2.
On one hand, (a^b)^c = ((−1)^2)^(1/2) = 1^(1/2) = 1.
On the other hand, a^(bc) = (−1)^(2*1/2) = (−1)^1 = −1.
So exponential rules may not work when the base isn't positive.
Then general rule that your argument relies on is that x^(a−b) = x^a/x^b. This rule actually holds pretty well for most numbers, but it does not hold when x = 0 _at all,_ regardless of the values of a and b. If this rule were valid for x = 0, we could also say, for instance,
0^2 = 0^(4−2) = 0^4/0^2 = 0/0, which is impossible. We would then conclude that 0^2 is undefined. Of course, 0^2 is very well-defined and has a universally agreed upon value of 0. So this argument can't be right. And you can go through the steps of this argument. The only thing that isn't absolutely solid is moving from 0^(4−2) to 0^4/0^2.
0^0 is a bit of a pet peeve of mine because tons and _tons_ of mathematicians agree that 0^0 = 1 is the best way to handle the situation. If you're working in a "discrete" branch of mathematics (one that doesn't focus on continuity), then 0^0 = 1 will _always_ work in _every_ formula where it arises. You only get into trouble with 0^0 when you confuse limiting forms with arithmetic and assume all functions must be continuous on their domains (which is false). Yet there are still many _mathematicians_ who perpetuate bad arguments about 0^0 and argue that is has to be undefined, despite (discrete) mathematicians' knowledge otherwise. (This is not an attack on _you._ It's an attack on people who _should_ know better because they have been exposed to this way of thinking already.)
A number divided by zero lacks an equation. The person asking
"What does 5 ÷ 0 = ?"
Is like him asking,
"What does 5"?
See? When zero follows the division symbol then no equation takes place. We've left the realm of mathematics and returned back to language. I'm surprised that I've never seen this explanation offered before. It is however the only one that explains the question.
When we attempt to divide by 0 we're no longer dividing. Its like any attempt to divide with zero automatically erases the whole procedure.
This is true for processors and the DIV instruction, when you try to divide by 0 there it fires an interrupt that basically means "Result is undefined". (It basically checks if there's a 0 anywhere in the 'equation', and if there is, it doesn't calculate anything) I'm not sure if that's true for all processors, but the ones I have experience with use the interrupt method.
I find I don't understand what you're saying here, which concerns me as you say that it's the only phrasing that successfully answers the question. How is it that you're able to say that "divided by zero equals" is equivalent to saying nothing at all? If math has proven capable of making proper use out of numbers that don't even exist (square root of negative one, an imaginary number), then why does this simple utterance disappear when nothing else does?
When he said, "For all we know, this line may wrap around the entire universe and connect" (paraphrased a bit), that got me thinking.
It can't, and here's why.
What mathematicians do to prove certain postulates or theorems occasionally is that they assume the end as an axiom, so let's assume that the number line does, indeed, wrap around the universe and connect end to end. Well, we also assume by this and the limit equation at about 5:00 that infinity is on one end and negative infinity is on the other. If this line wraps all the way around, end to end, and treating the respective infinities as the points on the line where it terminates, this would mean that infinity and negative infinity are adjacent to each other on this line. Not only are they adjacent, but there are also no numbers between them. There is no value that is greater than infinity (because x + infinity = infinity, whereas x = all real number) and no value is less than negative infinity (because negative infinity - x = negative infinity, whereas x = all real numbers). Because there is no value greater than infinity, it can't be possible to count up from infinity to negative infinity. And you can't count down to get to positive infinity.
Another issue would be that the function 1/x approaches positive infinity from the right and negative infinity from the left. This sentence treats infinity as a location, not a number, just as they say in the video. Infinity is not a number and cannot be treated as such. But saying that it is at the end of the number line and connects both sides means that there is a terminal location for infinity, which there isn't. (Terminal meaning simultaneously that there is a singular value that we can point to and say that is this number and that it is at the end of the line.) Infinity has no conclusive end to it because there are many ways to represent infinity, such as:
1+2+3+4+5+6....ad infinitum
*also*
2+4+6+8+10+12....ad infinitum
*therefore*
1+2+3+4+5+6....ad infinitum = 2+4+6+8+10+12....ad infinitum
Both of these number sets add to infinity. But one number set is clearly twice as large. If you wish to simplify it, this can also be represented by infinity = 2 x infinity. How can a number, cardinal or ordinal, be multiplied by any number other than 1 and still be equal to itself?
Short answer, it can't.
Long answer, it caaaaaaaaaaaaaaaaaaaaaaaaaaaan't.
*In conclusion*
There is no way to mathematically represent the fact that the number line wraps around. These problems have to be addressed for that to be true, and so far that's not possible, if it ever could be.
Also, due to the number line wrapping around, it would also be true that negative infinity and infinity are equal, but I don't know how to prove that. I just intuitively know it.
Thank you for coming to my TedTalk.
Wow, that's a long comment
Doesn’t the real number line pretty much wrap around in a real-number cross-section of the Riemann Sphere?
Also, 0 can be multiplied by any number and still equal itself. In fact, it can’t be otherwise. Or are you saying that 0 is not a cardinal or ordinal number?
@@paulchapman8023 I don't know anything about the Reimann Sphere, so I can't argue it's importance (though that doesn't mean it has none). As for zero, I genuinely hadn't considered it, despite the fact that it is cardinal and ordinal. It feels like a cop out of an answer to call it a special case, but i can't think of it any other way. Given its other exceptions (can't divide by it, exponential is 1 always, etc), I don't think its unfair to label it special and consider it separately in some other proof.
That was a great question, for a long ago i made this comment I still can tell I hadn't considered zero at all, thank you for bringing it up!
If 1/0 equals infinity, the that means infinity times 0 equals 1, which is not possible.
0χ(+-infinity) is an undefined number so it can be 1 as well
You can't just treat infinity as any other number. It is an idea, not a value you can do operations on.
I did not say that infinity is any number.I said 0x(infinity) is an undefined number so you dont know whether it is equal to 1 or not , therefore you can not say that 0x(infinity)=1 is an impossible equation, it is an undefined equation. And you can do operations on infinity. For example: (1/infinity)=0 and: (+infinity)(-infinity)=-infinity
+Tomas Cena I was refering to the main comment :)
DrDerp42
This is a dangerous subject
I always hated math and no one I know likes it, but it is nice to see people with a real passion and love for maths/numbers to make it more interesting
for x^x, doesn’t -1^-1 equal -1 or am i missing something?
@Mika Hamari That makes sense since X^-n is equal to 1/X^n and when n is even you get a positive number
Yes you are right it's equal to -1
Nope. You are correct.
Yea it does
Correct. But matt's sketch was terrible as it didn't require that detail.
I tried 1/0 on wolfram and it gave me
This Wolfram|Alpha server is temporarily unavailable.
lol
@TalkingTomKittyKatFan2021 Aka BAC Klapof No, it says it's complex infinity which is different.
3:16 infinity is actualy a duble zero :D Was that on purpos???
A CPU will actually stop the running program immediately when encountering a DIV0 and throw what‘s called an exception. A special part of the operating system will then take over and handle the exception, e.g. showing a blue screen.
If you look at zero in terms of inversion, zero is essentially "neutral infinity", in a way. If you take the inversion of zero with any base radius, you will get a variation of infinity as the answer.
I think you're confused in that you are making weird calculations based on our imperfect, artificially created interpretation of mathematics. Doing a bunch of maneuvers isn't proof that nothing is equal to everything, it's just a flaw in the math we created.
those are some weird x's
a^0 = 1 and 0^a = 0 can't both be true if a = 0, because then 1 = 0. So for that reason alone 0^0 can't be defined.
_This Comment is cross-posted!_
*0^x = 0* is _only_ true for _positive_ exponents!
_This Comment is cross-posted!_
1 is a more consistent answer. The *Taylor expansion* for e⁰ will be *0⁰/0! + 0¹/1! + 0²/2! + 0³/3! + ... = e⁰ = 1.* The only term that is not 0 is *0⁰/0!.* There is also the *Taylor expansion* for *cosine.* If *n* objects each have *k* states, then the equation for the number of the set's positions is *n^k.* Think about the number of positions that [a set of 0 objects each with 0 states] has. This is philosophical, but it is one state.
As for *0^x = 0,* that is only true for _positive_ exponents of 0. The Binomial Theorem also relies on the *0⁰ = 1* statement. As for limits, those are only accurate to the true value for continuous functions. Take the piecewise equation *y = x if x ≠ 5, y = 1 if x = 5.* The limit of y as x approaches 5 is 5, but *y = 1* AT *x = 5.* As for the *Product&Quotient Rules* of exponents, under certain circumstances, those are false for 0.
I hope this makes sense.
5:50 The look you get, when you're on a date with a mathematician
he’s rizzing us up 💀