@JimmyMontoya He definitely excels as a teacher, because he understands how a person learns. If a teacher does not understand how someone learns they are no teacher at all.
@@XiaoMof but how do you call people who were taught by mostly non-teachers? because we need a name for this type of humanity we're stuck with. if we don't come up with it, historians from the future surely will, if they ever come to be.
I haven't even watched the whole video yet, but i love how at around 0:30 you kill that chatter in the background without even saying a word and without breaking your train of thought. It wasn't even a particularly angry or threatening look either, but it perfectly got the point across.
That's what happens when a teacher is so good, and has earned the respect of all of his pupils... He allows a certain level of chatter as his pupils take the ideas on board, but doesn't let it stop the forward progress of the lesson.
I love it that an enthusiastic, young, Australian math teacher has almost a MILLION subscribers! I’m a subscriber and I haven’t taken a math course in many decades. He just makes it fun and interesting.
@@BeckBeckGo - I’m envious! That sounds pretty cool! One thing that rekindled my interest in math was the advent of home computers (yes, I’m old). It’s AMAZING how computers take the drudgery out of math. Can you imagine using a slide rule? Yuck!
@@BeckBeckGo - Oh, and if you decide to go into the private sector, be prepared for HUGE paychecks! Pure math has so many high-demand uses, you will be shocked at how much you will be making. Just a tip though: try to get some statistics and computer science in your repertoire (if you haven’t already).
Damn this guy is a fricking king. Makes a math class soooo much fun. I’d love to rewind time....jump on a plane to Australia just so I can have classes under him
He actually understands math which I think a lot of the teachers I had didn’t. Math is my biggest source for frustration and failure. And I love these videos!
You're a brilliant teacher dude, this entire generation can benefit from how you make the material inspiring and intriguing, keep doing what you're doing.
This guy is a Master Teacher. Every time I watch one of his math videos, I go "Woo". He always brings something you have taken for granted or just never thought about it, in a new perspective in a very simple way. I never thought of numbers in terms of sets, even though I have used both in math and elsewhere. Changes you entire perception of life. Thank you Mr Woo
Great progression through your topics. What I love is the way you safety-net each step. When I was at school/college, back in the day when white-hot technology was a quill, it was so easy to get to the stage in a lesson where the current concept on offer didn't quite find the mental hook that it was meant to hang on. The lecturer would already be onto the next part of the lesson and panic would set in. You have the wonderful knack of anticipating when those hooks haven't quite formed and providing that extra material.
The notion of a space and a vector isn't really reducible to sets. It can be defined in terms of sets, but you wouldn't be able to find anything in sets themselves that tell you that they can be graphically represented in any way at all.
@@lorax121323 Well, there is nothing in the number 3 that tells you that it can be represented graphically either. That doesn’t stop us from drawing 3 dots, 3 cows or 3 vectors.
For the record: Atoms are indivisible in the sense that if you take a block of iron, and cut it in two, you have two blocks of iron. If you take two atoms of iron and cut in two, you have two separate atoms of iron. If you take an atom of iron and cut in two, it's no longer iron.
@@AzureKyle Not in the case of iron, too stable. You'd just get 2 silicon nuclei or something. But the point is it's no longer iron. An atom can be divided, but only by changing its nature.
I would say that sets breaks down to counting, then comes "Haves and Have-nots." Which can be presented as 1 and 0. Now all are operations stem from counting. So addition use counting of the sets, and subtraction is the opposite but still is counting. Now multiplication is faster adding which goes down to counting. Then once again, division is the opposite but is still counting. If you want you can include any operations, and they will break down to counting then too "Haves and Have-nots." One more example is exponents, which is faster multiplication and it breaks down..... Now the opposite would be roots. This is the whole computer world 0 and 1.
The more technical answer to "what are negative numbers?" which was asked in class is: take the set of ordered pairs of non-negative numbers (so (1, 2) is different from (2, 1)). Then calculate the difference between them, in the above case, the difference is 1. An integer number is the set of all pairs of whole numbers with the same difference. So (5, 3) and (8, 6) are both in the set representing the integer "2". And you can check that addition and such works, regardless of which pair you choose: (5, 3) + (8, 6) = (13, 9) says that 2 + 2 is 4, even though we chose different pairs to represent the number 2. A negative number is just the same thing, but in the case where the second number is larger than the first number. So (5, 3) is part of 2, but (3, 5) is part of -2. And again, you can check. (3, 5) + (8, 6) = (11, 11) says that -2 + 2 = 0. Of course, this is not how anyone actually thinks about negative numbers: the point is that, in mathematics, we always want to avoid contradictions. Checking that this works tells us that, provided there are no contradictions in the positive numbers, a simple structure, then there are no contradictions in the negative numbers, which are more complicated.
Would love to watch a documentary similar to the Brit show "63 up" (but not wait so long) where some of Eddie Loo's students are interviewed to see where they are now and what they are doing. His teaching style is so *_engaging_*, I can imagine a number of students found him and his class inspirational.
Regarding the "if you have a headache thinking about infinity, that's probably a good thing" introduction: there's an infamous story that Gregor Cantor himself went mad dealing with infinities. While that's a bit reductive, there is some truth to it: Cantor was bipolar, and between the stress of his work and the stress of his colleagues dismissing his work, it aggravated his symptoms. So if you feel like dealing with infinities is too stressful and driving you mad, you're in great company! 😁
That's like a dream class to be in ! The students are also joining in to spiral their ideas and ask the what ifs and it's interesting to listen to every questions.It gives much more information and curiosities to be answered. A real great dedicated teacher. My respect to you on being able to make the students become enthusiastic!
There should be the "Woo" standard named in honor of Eddy & any teachers NOT achieving this standard of teaching excellence, should get retrained or told to try a different career path! Some of my teachers had all the energy & motivation of a stone! How can the likes of these motivate & inspire their students? Eddy makes maths not just interesting but real FUN!!!
The correct answer is the laws of logic (identity, contradiction, excluded middle). The only inviolate rule of math is: contradiction is forbidden. Set theory is a formalization of identity and non-contradiction.
Surely "laws of logic" go beyond math. Should we call math “quantitative reasoning” or do we more narrowly restrict it to axiomatic set theory? Moreover, it seems like you are taking sides on Gödel's incompleteness theorems. What if it’s useful to have contradiction and/or incompleteness?
The laws of logic do go beyond math and that is the point to why math is a higher level language. And contradictions and incompleteness on still follow proper logic on lower levels. It's like comparing a red apple to a red car and calling it beautiful simply because there is room for beauty and randomness even though it is similar... it's not similar you're simply making a higher level distinction. If you look at the number of atoms, for example, which make up the colors, they are vastly different and they aren't different in a different way, they are different in a fundamental way. So knowing that, the only time it's useful to have a contradiction in math is when you are looking for the contradiction so you're looking for a certain set which is covered in math as a logical principle.
Robert Rauch which laws of logic? Because just like you can build numbers from mathematical objects other than sets, you can also do that building with different logics.
Mathematical logic constantly uses mathematical induction, and for that you need a highly developed theory of natural numbers. So the basic building block is numbers; the students were right.
Maths is a subject where the quality of the teacher really, really makes a difference. I hate maths but his lectures are great to watch. A master class in creating engagement.
My response would be: quantities. Numbers are just one way of expressing quantities, but they aren't the only way. Now going to watch further to find out the actual answer ☺
Thank goodness he understands that teaching is SO much more than the subject matter. If there were only more people in every profession that cared and tried as hard as he does....the world would be a much better place for “life”.....I also believe he is a life long “learner”...and communicates that to his students through his enthusiasm, teaching, and humility....
If you have transferred some knowledge to one person in a group with whom you are communicating you have done a wonderful thing - listen to the response from one individual in the class at 15:45 or 15:46.
Events are the basic building block of special relativity. Binary numbers - equivalently, Boolean algebras - constitute the basic building block of mathematics - including logic and category theory (even of non-binary logic)!
I was waiting for him to hold up 3 markers and then take 4 away to demonstrate what -1 looks like! I wasnt entirely convinced the analogy with matter helped because there you are subdividing something down into smaller and smaller elements but with Mathematics there are a number of concepts such as symbols, rules (axioms), sets, groups etc that complement each other. Is the building block of language letters?, symbols? grammar?
Same. I actually had the same reaction (but with my inside voice) and it was so funny to hear. Not because I didn't get negative numbers so much as just that way of showing the 'weird' negative result of an arithmetic operation can be rearranged into something that looks perfectly intuitive and routine to most people - but *it's the same thing.*
If phyiscs is the language to describe the *patterns of nature* , then mathematics is the language to describe *patterns* in and of themselves. The axioms of what patterns are is based on observations of patterns. So what are patterns? Maybe one way to define it is *that which is consistent*
the whole goal of division is to subtract until you get 0. if you subtract by 0, you wont be able to change anything and be unable to reach your goal. thus anything divided by 0 should be classified as "you're missing the point" and 0 divided by 0 equals 0 because you're already there.
I'd have thought that 0/0 is still undefined, because you can take an infinite number of zeros away from zero and still have zero, so the fact that you're already there doesn't change the fact that dividing by zero is impossible.
I would say that division by zero is undefined due to the definition of division and the definition of zero. Division is to break up or divide a number by another number. Zero is a number that represents nothing. Dividing by zero is to divide by nothing, which is essentially trying to divide by not dividing, since dividing by nothing is the same as not dividing in the first place. Thus, division by zero, by he definitions of division and zero, violates the law of non-contradiction, which is one of the key logic laws that mathematics follows.
Late to the party, but my 2c: I think you can get a decent amount of math from 4 things: 0, incrementation (adding 1), repetition, and inverse (opposite operation). From 0, repeated incrementation produces addition and the natural numbers. The inverse of addition (or the repetition of the inverse of incrementation) produces subtraction and the negative numbers. Repeated addition produces multiplication. The inverse of multiplication produces division, and the rational numbers. Repeated multiplication produces exponents. The exponential function can be inverted in two different ways to produce the root and logarithm functions, complex numbers, and a more (but not all?) of the real numbers.
I always thought maths was built on and about relationships. When i was little, numbers were alive to me, i saw maths questions as a beautiful multiple dimensional reality ( that literally looked to me like a bluish spece in constant motion, from which all could be derived and brought into focus and harmony.) I was always correct on my work. Then my grade 3 teacher, a grumpy womanwho never smiled,tookpleasure in publically humiliating me because i didnt follow her methods on paper. And i became phobic about maths. This is the first time since then (and i am 51) that i have enjoyed maths.
Because methods are much more important than you think. Of course there are multiple ways to solve a problem!! BUT classical education requires mastery of multiple methods and not just one which was the most comfortable for you.
@@fbiagent6456 Properly understanding math requires knowing how different methods should arrive at the same conclusions if they follow the same set of premises. If they arrive upon different conclusions, then it indicates that they differ in their defining axioms. The point of traditional education is the dissemination of one set of facts and at least one definite way of dealing with them, regardless of whether or not students can even conceive the possibility of other methods existing.
my answer was add and subtracting, because no matter what you use, real numbers or imaginary or even letters, the thing that makes math math is the interaction between those elements. and adding and subtracting seem to me like the most basic one, all the other actions like dividing or multiplying are made from them.
Other answers I have by the 12:36 mark (so still waiting for the rest of the video to finish) include maybe one of the following if not logic or imagination haha: (1) relationships (2) patterns (3) categories (4) abstraction
Such a great teacher! Love your videos. Don’t know him, but seems like such a great man. Someone who can approach these things with that passion. The world needs more Eddie Woo’s.
Hey Dr. Woo! I got an idea. Let's make 1 the building block of *all* of arithmetic! We'll make everything else from it with a single operation - perfectly suited for balancing accounts - that we call "take-away", and denote it as "−". Every number, we shall decree, can be formed from 1 by taking combinations of take-away operations with it. We will impose two conditions: (a) for all numbers a, b: a − (a − b) = b, (b) for all numbers a, b, c: a − (b − c) = c − (b − a). We'll *define* the number 0 as 1 − 1 and call it the "break even" number. We'll then *prove* as a theorem that (c) for all numbers a: a − a = 0. Proof: a − a = 1 − (1 − (a − a)) = 1 − (a − (a − 1)) = 1 − 1 = 0, by applying (a), (b), (a) and the definition of 0. We'll *define* the "take-away" of a number as -a = (a − a) − a and use the theorem to prove that 0 − a = -a. Then, we'll define the *sum* of two numbers as a + b = a − -b and ... with these definitions ... prove that we have *all* the basic laws of arithmetic for the operations of plus and minus. For instance, a + 0 = a − -0 = a − (0 − 0) = 0 − (0 − a) = a and 0 + a = 0 − -a = 0 − (0 − a) = a ... using the axioms and results proved up to this point.
When he talks about the English numbers 1,2,3, they are actually based on counting the number of angles in the written symbol, not on counting the number of straight lines in the written symbol. The number one (1), if you look carefully at it, has one angle inside it, and the number (2) has two angles in it, and so on, and so forth. Look at the number (8). If you write it without curves, it has eight right angles inside it. etc
It's awesome that you're able to devote class time to so many fascinating topics outside the core curriculum. I've talked to high school teachers who say they're really constrained by the need to cover a mandated list of topics and prepare students for standardized tests. I'd be interested to hear how you navigate this issue.
The way he plays with sets he's actually just talking about the cardinality of sets (which are actually numbers). So sets require (natural) numbers, and the basic blocks for those are the prime numbers.
My first instinct was indeed numbers, but then I thought it was 1, with everything being derived from the concept of 1. Then I thought it was definition (since 0 didn't seem to fit in with that) - using numbers to specify/understand something, like distance or an amount of time, and how they interact.
If only the history teacher I had was even half as good as he is... The building blocks of mathematics are axioms by the way and numbers are symboles used to represent the cardinality of sets.
JustSaying 21 Logic is a tool in mathematics. You put in some axioms and use logic to build your mathematics from that. It's like axioms are the basic building blocks and logic is the fundamental forces
An atom is the smallest fragment of a given element. It can not be divided into smaller fragments of the same element. So the word still orks as a definition.
Almost got this right. The fundamental building block of numbers is proportions. Of actually all reality. It's a way of communicating/defining proportion. It's the language of Creation, and Creation is about differentiating the whole into parts.
My answer during the time when everyone else was shouting out: Logic (I was juggling up between this answer and imagination - logic after all creates the orderly sequence of numbers that we know as positive integers and otherwise) Will be interesting to see what the rest of the video shows haha great stuff :-)
I think that too, in fact when you prove things you don't use sets. Especially proving mathematical logic and stuff. His title is not technically true since he wrote "all mathematics".
I would say logic must be applied to something for it to become math, so I wouldn't call it a building block. It's like the mortar rather than the brick. Of course you it's what allows you to build, but it's not the thing you're building with.
@@andrewprahst I would disagree, slightly. Logic is inherent. It need not be applied to something for that something to manifest naturally and systematically. Logic is what allows us to distinguish this from that, label and categorize them. You are correct in that logic isn't a building block - but it is the fundamental process that allows us to understand what the fundamental building block might be. To me, it's zero and I also consider zero = infinity.
Hi Mr. Woo. You're right. There are many different origins of mathematics and science. For example, what's the basic building block of a computer. You start to tear it apart, and you find various circuit boards, such as the CPU (central processing unit), input, output, memory, storage, operating system, etc. There are building blocks of everything you see, such as computer software. If you dig deeper into it without using a scanner or an x-ray, you'll find binary code, which is the basic building block of computer software.
Maybe? The incompleteness theorems show that infinite extension of the axioms can be insufficient for a problem, and I think corollaries of the axioms can have computational cost. Reduction to first order logic seems, to me, to be equivalent to the assumption that the total system never changes. I wonder if change is necessary to our existence; A perfectly reversible system can be used for perpetual motion! Such a system might exist, but I would not expect to find one available for experiment.
Neither of us needs to be accredited when we're just sharing our interest in the subject. If there's something wrong with what I'm saying, I'd love to hear about it.
It's amazing high school kids have the opportunity to have a teacher like him lol. When I was in high school, our teacher was half asleep dragging through trig. This man is teaching his students things I didn't see until a fair way into university. Great guy tbh
My grandmother taught me about infinity when I was a toddler. So to me it made perfect sense. I had asked her what the biggest number was. She told me to guess and I said some number and she then said there was always a next number, forever. Blew my little mind.
What makes up Math? The equilibrium around numbers such as Pi, i, and e. Numbers are units we made up, but in the end it's just a balance of the numbers around equilibrium to come to an answer.
I think the basic building block of math is the concept of a whole, or one. Numbers arise when you need to keep track of more than one, operators arise when you start thinking of numbers abstractly, and new kinds of numbers arise when you start thinking of operators abstractly.
I hope I get to meet this guy one day...His brain's programmed to impart knowledge so effectively, systematically and logically to his students....using Logic!!!
Number are just used to represent something. In binary system we use 1 and 0 to represent a particular no. We use diff permutation of combination of 0 and 1 to represent no.
I would say sets are the basic elements of mathematics. However, I think mathematics is about problem solving and modelling thing. And it is done by doing things with rules - algorithms. Creating more general rules and algorithms is a way of creating general models. It is one of the things what e.g. mathematicians do. And proving is the way of checking whether that model is good enough model.
Might even be able to say: just like we use words, we may use these other, names/words?, and put them together in different ways to say certain things? A possibility perhaps. Words are as empty, or, grammar structures are very much like algebraic variables, but more familiar to them.
It's called Subitizing. After that, addition (combining sets) and multiplication (sets of sets). From there, we just make crap up as problems arise to remain consistent.
I would have said the basic building blocks were "operations". Numbers and Sets are fundamental, but on their own they are just data. they're not information, they're not math. They are just values without context or use. It's only when they are being related to something that they contribute meaning. Operations might involve multiple numbers/values, but they are what create the context and meaning that makes math math. Hell, even picturing "3" as presented here, as "the number of members of this set of three objects" is in itself an operation: equals/assignment. 3==[cup, cup, cup] for example.
I can not express how mind blown I am after watching this video . I discovering Eddie Woo's channel from a suggested video after 3brown1blue video that talked about group theory. Coming into this video thinking the basic building blocks of math being ratio's and portions(negatives are reflections and imaginary are laterals) gave me the understanding that dividing by 0 would take away the starting point or cancel out measurement (I thought of 3browns1blues linear scale). I sat in my chair mind blown not knowing if I was peaking from the weed or actually having an epiphany. I thought dividing by 0 would create unmeasurable chaos. After watching his next video to find out why dividing by 0 is undefined I feel so inspired after this I feel i have direction and want to pursue a degree in math.
I personally always thought the basic building block of maths was 'definitions'. Because definitions of different terms used in mathematics are what set the boundaries that allow for the interpretation of mathematical rules & equations. The definition of what a number is allow them to be used in a comprehensible manner. The definition of a line allows for the existence of 2 dimensional & 3 dimensional shapes and the rules you can create in combination with the definition of lines & numbers is what is necesary for the creation of trigonometry.
![Blox Fruits Dragon Rework Update [Full Stream]](http://i.ytimg.com/vi/EqDAp8udhm0/mqdefault.jpg)
you know he's a good teacher when he's got me watching these videos for fun
Same here...it's so much fun
Yes, he is interesting and motivate students to learn.
Literally was going to say.. "Sometimes I watch these videos for entertainment." You got me bro lol.
same
Same
I think Eddie Woo might just be the basic building block of education!
This is what a great educator look like!
@JimmyMontoya He definitely excels as a teacher, because he understands how a person learns. If a teacher does not understand how someone learns they are no teacher at all.
@@XiaoMof but how do you call people who were taught by mostly non-teachers? because we need a name for this type of humanity we're stuck with. if we don't come up with it, historians from the future surely will, if they ever come to be.
I think “non teachers” are a fact of life that nobody can really escape.
"I don't want you to shout out any answers."
Mr. Woo is flexing on us with how much engagement he's getting.
I haven't even watched the whole video yet, but i love how at around 0:30 you kill that chatter in the background without even saying a word and without breaking your train of thought. It wasn't even a particularly angry or threatening look either, but it perfectly got the point across.
That's what happens when a teacher is so good, and has earned the respect of all of his pupils... He allows a certain level of chatter as his pupils take the ideas on board, but doesn't let it stop the forward progress of the lesson.
I am a retired instrumentation technician and a Maths lover....I must say this guy is a wonderful teacher. :)
Desire Bruno Duval
Do you realize that reality is based on logic and reason.
??
@@gretawilliams8799 are u against him? just asking
YEAH, I wish that I could have a teacher like him, when I was at school. XD
@@gretawilliams8799 Not always! Reality is also perspective, intuition, and will power!
Desire Bruno Duvel - That sounds like a decent job how do you get into that? Electrical engineering? A certain trade?
"But what is three?"
*vsauce music kicks in*
I wanted to say it was a concept.
@@TheMistforman You're thinking of infinity :)
@@TheMistforman , you are quite right. "3" represents a concept.
3 is a "Name".
@@fazalahmed2329 “3” is an amount.
“3” is a number
“Three” is a word
I love it that an enthusiastic, young, Australian math teacher has almost a MILLION subscribers! I’m a subscriber and I haven’t taken a math course in many decades. He just makes it fun and interesting.
Hell I’m a student of pure mathematics and I watch this guy teach high school.
@@BeckBeckGo - I’m envious! That sounds pretty cool! One thing that rekindled my interest in math was the advent of home computers (yes, I’m old). It’s AMAZING how computers take the drudgery out of math. Can you imagine using a slide rule? Yuck!
@@BeckBeckGo - Oh, and if you decide to go into the private sector, be prepared for HUGE paychecks! Pure math has so many high-demand uses, you will be shocked at how much you will be making. Just a tip though: try to get some statistics and computer science in your repertoire (if you haven’t already).
There’s a mil of us now boooiiiii
>division by zero
>YEEESSS
wow that is some enthusiastic student. Probs.
Hahaha
Fuck off then
@@gretawilliams8799 bruh
Damn this guy is a fricking king. Makes a math class soooo much fun. I’d love to rewind time....jump on a plane to Australia just so I can have classes under him
yea his best videos are from 2014-2016
He actually understands math which I think a lot of the teachers I had didn’t. Math is my biggest source for frustration and failure. And I love these videos!
Same here. 😠 I try to keep calm nowadays about this fact as anger can't repair the damage already done.
For some reason I always imagined the door on the other side of the room
You're a brilliant teacher dude, this entire generation can benefit from how you make the material inspiring and intriguing, keep doing what you're doing.
This guy is a Master Teacher. Every time I watch one of his math videos, I go "Woo". He always brings something you have taken for granted or just never thought about it, in a new perspective in a very simple way. I never thought of numbers in terms of sets, even though I have used both in math and elsewhere. Changes you entire perception of life. Thank you Mr Woo
Great progression through your topics. What I love is the way you safety-net each step. When I was at school/college, back in the day when white-hot technology was a quill, it was so easy to get to the stage in a lesson where the current concept on offer didn't quite find the mental hook that it was meant to hang on. The lecturer would already be onto the next part of the lesson and panic would set in. You have the wonderful knack of anticipating when those hooks haven't quite formed and providing that extra material.
The two primitive “building blocks” of math are sets, and the relation “is an element of”, that tells us if something is or is not “in” a set.
The notion of a space and a vector isn't really reducible to sets. It can be defined in terms of sets, but you wouldn't be able to find anything in sets themselves that tell you that they can be graphically represented in any way at all.
@@lorax121323 Well, there is nothing in the number 3 that tells you that it can be represented graphically either.
That doesn’t stop us from drawing 3 dots, 3 cows or 3 vectors.
For the record: Atoms are indivisible in the sense that if you take a block of iron, and cut it in two, you have two blocks of iron. If you take two atoms of iron and cut in two, you have two separate atoms of iron. If you take an atom of iron and cut in two, it's no longer iron.
Exactly. It's no longer iron, it's an explosion.
@@AzureKyle Not in the case of iron, too stable. You'd just get 2 silicon nuclei or something. But the point is it's no longer iron. An atom can be divided, but only by changing its nature.
@@MadaraUchihaSecondRikudo I was making a joke, because usually when you split an Atom, it causes a nuclear reaction.
@@AzureKyle Yes, but not iron atoms :D, they don't cause a reaction since they're too stable.
I would say that sets breaks down to counting, then comes "Haves and Have-nots." Which can be presented as 1 and 0. Now all are operations stem from counting. So addition use counting of the sets, and subtraction is the opposite but still is counting. Now multiplication is faster adding which goes down to counting. Then once again, division is the opposite but is still counting. If you want you can include any operations, and they will break down to counting then too "Haves and Have-nots." One more example is exponents, which is faster multiplication and it breaks down..... Now the opposite would be roots. This is the whole computer world 0 and 1.
The more technical answer to "what are negative numbers?" which was asked in class is: take the set of ordered pairs of non-negative numbers (so (1, 2) is different from (2, 1)). Then calculate the difference between them, in the above case, the difference is 1. An integer number is the set of all pairs of whole numbers with the same difference. So (5, 3) and (8, 6) are both in the set representing the integer "2". And you can check that addition and such works, regardless of which pair you choose: (5, 3) + (8, 6) = (13, 9) says that 2 + 2 is 4, even though we chose different pairs to represent the number 2. A negative number is just the same thing, but in the case where the second number is larger than the first number. So (5, 3) is part of 2, but (3, 5) is part of -2. And again, you can check. (3, 5) + (8, 6) = (11, 11) says that -2 + 2 = 0. Of course, this is not how anyone actually thinks about negative numbers: the point is that, in mathematics, we always want to avoid contradictions. Checking that this works tells us that, provided there are no contradictions in the positive numbers, a simple structure, then there are no contradictions in the negative numbers, which are more complicated.
Would love to watch a documentary similar to the Brit show "63 up" (but not wait so long) where some of Eddie Loo's students are interviewed to see where they are now and what they are doing. His teaching style is so *_engaging_*, I can imagine a number of students found him and his class inspirational.
My answer to the question was addition/subtraction. Multiplication and division is just addition/subtraction ... done over and over.
Regarding the "if you have a headache thinking about infinity, that's probably a good thing" introduction: there's an infamous story that Gregor Cantor himself went mad dealing with infinities. While that's a bit reductive, there is some truth to it: Cantor was bipolar, and between the stress of his work and the stress of his colleagues dismissing his work, it aggravated his symptoms. So if you feel like dealing with infinities is too stressful and driving you mad, you're in great company! 😁
That's like a dream class to be in ! The students are also joining in to spiral their ideas and ask the what ifs and it's interesting to listen to every questions.It gives much more information and curiosities to be answered. A real great dedicated teacher. My respect to you on being able to make the students become enthusiastic!
As a professor, I can say that you are an inspiration to me. Congrats on being an amazing human being. Love from Brazil!
There should be the "Woo" standard named in honor of Eddy & any teachers NOT achieving this standard of teaching excellence, should get retrained or told to try a different career path! Some of my teachers had all the energy & motivation of a stone! How can the likes of these motivate & inspire their students? Eddy makes maths not just interesting but real FUN!!!
Given the way societies tend to treat teaches, it's amazing any of them can be enthusiastic for more than a couple years. :(
Pop smoke
At least we have the internet to allow great teachers the recognition they deserve.
i like your class i havent had a teacher that was engaging and this fun to learn from since a while. thank you for your hard work and effort!
What an awesome interacting class.I wish mine was like this
The correct answer is the laws of logic (identity, contradiction, excluded middle). The only inviolate rule of math is: contradiction is forbidden. Set theory is a formalization of identity and non-contradiction.
Surely "laws of logic" go beyond math. Should we call math “quantitative reasoning” or do we more narrowly restrict it to axiomatic set theory? Moreover, it seems like you are taking sides on Gödel's incompleteness theorems. What if it’s useful to have contradiction and/or incompleteness?
The laws of logic do go beyond math and that is the point to why math is a higher level language.
And contradictions and incompleteness on still follow proper logic on lower levels. It's like comparing a red apple to a red car and calling it beautiful simply because there is room for beauty and randomness even though it is similar... it's not similar you're simply making a higher level distinction. If you look at the number of atoms, for example, which make up the colors, they are vastly different and they aren't different in a different way, they are different in a fundamental way.
So knowing that, the only time it's useful to have a contradiction in math is when you are looking for the contradiction so you're looking for a certain set which is covered in math as a logical principle.
I'd like sets for 200 please
Robert Rauch which laws of logic? Because just like you can build numbers from mathematical objects other than sets, you can also do that building with different logics.
Mathematical logic constantly uses mathematical induction, and for that you need a highly developed theory of natural numbers. So the basic building block is numbers; the students were right.
Maths is a subject where the quality of the teacher really, really makes a difference. I hate maths but his lectures are great to watch. A master class in creating engagement.
My response would be: quantities. Numbers are just one way of expressing quantities, but they aren't the only way. Now going to watch further to find out the actual answer ☺
15:45 the knowledge has reached his destination.
I just love that the reaction you get out of your class for this complicated subject is "Yes!'... such a beautiful question.
Great teacher. Reminds me of the philosophy of statistics and probability course i took.
1.digits
2.symbols
3.relation
4.logic
5.pattern
6.imagination
Thank goodness he understands that teaching is SO much more than the subject matter. If there were only more people in every profession that cared and tried as hard as he does....the world would be a much better place for “life”.....I also believe he is a life long “learner”...and communicates that to his students through his enthusiasm, teaching, and humility....
If you have transferred some knowledge to one person in a group with whom you are communicating you have done a wonderful thing - listen to the response from one individual in the class at 15:45 or 15:46.
Events are the basic building block of special relativity.
Binary numbers - equivalently, Boolean algebras - constitute the basic building block of mathematics - including logic and category theory (even of non-binary logic)!
Super interesting class sir you are not a human
You are a machine full of ideas
I was waiting for him to hold up 3 markers and then take 4 away to demonstrate what -1 looks like! I wasnt entirely convinced the analogy with matter helped because there you are subdividing something down into smaller and smaller elements but with Mathematics there are a number of concepts such as symbols, rules (axioms), sets, groups etc that complement each other. Is the building block of language letters?, symbols? grammar?
That girl from 15:45 it's me in every class when i finally understand something LOL
Oooh.
Same. I actually had the same reaction (but with my inside voice) and it was so funny to hear. Not because I didn't get negative numbers so much as just that way of showing the 'weird' negative result of an arithmetic operation can be rearranged into something that looks perfectly intuitive and routine to most people - but *it's the same thing.*
If phyiscs is the language to describe the *patterns of nature* , then mathematics is the language to describe *patterns* in and of themselves.
The axioms of what patterns are is based on observations of patterns.
So what are patterns?
Maybe one way to define it is *that which is consistent*
the whole goal of division is to subtract until you get 0. if you subtract by 0, you wont be able to change anything and be unable to reach your goal. thus anything divided by 0 should be classified as "you're missing the point" and 0 divided by 0 equals 0 because you're already there.
I'd have thought that 0/0 is still undefined, because you can take an infinite number of zeros away from zero and still have zero, so the fact that you're already there doesn't change the fact that dividing by zero is impossible.
I would say that division by zero is undefined due to the definition of division and the definition of zero. Division is to break up or divide a number by another number. Zero is a number that represents nothing. Dividing by zero is to divide by nothing, which is essentially trying to divide by not dividing, since dividing by nothing is the same as not dividing in the first place.
Thus, division by zero, by he definitions of division and zero, violates the law of non-contradiction, which is one of the key logic laws that mathematics follows.
Late to the party, but my 2c: I think you can get a decent amount of math from 4 things: 0, incrementation (adding 1), repetition, and inverse (opposite operation). From 0, repeated incrementation produces addition and the natural numbers. The inverse of addition (or the repetition of the inverse of incrementation) produces subtraction and the negative numbers. Repeated addition produces multiplication. The inverse of multiplication produces division, and the rational numbers. Repeated multiplication produces exponents. The exponential function can be inverted in two different ways to produce the root and logarithm functions, complex numbers, and a more (but not all?) of the real numbers.
I always thought maths was built on and about relationships.
When i was little, numbers were alive to me, i saw maths questions as a beautiful multiple dimensional reality ( that literally looked to me like a bluish spece in constant motion, from which all could be derived and brought into focus and harmony.) I was always correct on my work. Then my grade 3 teacher, a grumpy womanwho never smiled,tookpleasure in publically humiliating me because i didnt follow her methods on paper. And i became phobic about maths. This is the first time since then (and i am 51) that i have enjoyed maths.
Because methods are much more important than you think. Of course there are multiple ways to solve a problem!! BUT classical education requires mastery of multiple methods and not just one which was the most comfortable for you.
@@fbiagent6456 Properly understanding math requires knowing how different methods should arrive at the same conclusions if they follow the same set of premises. If they arrive upon different conclusions, then it indicates that they differ in their defining axioms. The point of traditional education is the dissemination of one set of facts and at least one definite way of dealing with them, regardless of whether or not students can even conceive the possibility of other methods existing.
I would have answered that the basic building blocks of maths are the axioms we have chosen.
my answer was add and subtracting, because no matter what you use, real numbers or imaginary or even letters, the thing that makes math math is the interaction between those elements. and adding and subtracting seem to me like the most basic one, all the other actions like dividing or multiplying are made from them.
Other answers I have by the 12:36 mark (so still waiting for the rest of the video to finish) include maybe one of the following if not logic or imagination haha:
(1) relationships (2) patterns (3) categories (4) abstraction
Such a great teacher! Love your videos.
Don’t know him, but seems like such a great man. Someone who can approach these things with that passion. The world needs more Eddie Woo’s.
Hey Dr. Woo! I got an idea. Let's make 1 the building block of *all* of arithmetic! We'll make everything else from it with a single operation - perfectly suited for balancing accounts - that we call "take-away", and denote it as "−". Every number, we shall decree, can be formed from 1 by taking combinations of take-away operations with it. We will impose two conditions:
(a) for all numbers a, b: a − (a − b) = b,
(b) for all numbers a, b, c: a − (b − c) = c − (b − a).
We'll *define* the number 0 as 1 − 1 and call it the "break even" number. We'll then *prove* as a theorem that
(c) for all numbers a: a − a = 0.
Proof: a − a = 1 − (1 − (a − a)) = 1 − (a − (a − 1)) = 1 − 1 = 0, by applying (a), (b), (a) and the definition of 0.
We'll *define* the "take-away" of a number as -a = (a − a) − a and use the theorem to prove that 0 − a = -a.
Then, we'll define the *sum* of two numbers as a + b = a − -b and ... with these definitions ... prove that we have *all* the basic laws of arithmetic for the operations of plus and minus. For instance, a + 0 = a − -0 = a − (0 − 0) = 0 − (0 − a) = a and 0 + a = 0 − -a = 0 − (0 − a) = a ... using the axioms and results proved up to this point.
What a role model for young people.Learning is fun -you just need the right person to lead,guide,coach and encourage
I'm a computer science student and no longer need to do maths but here I'm enjoying your videos i miss doing maths.
Wonderfull!!
When he talks about the English numbers 1,2,3, they are actually based on counting the number of angles in the written symbol, not on counting the number of straight lines in the written symbol. The number one (1), if you look carefully at it, has one angle inside it, and the number (2) has two angles in it, and so on, and so forth. Look at the number (8). If you write it without curves, it has eight right angles inside it. etc
They way the class goes “yesssss” when he writes on the board division by zero, tells you a lot about the kind of teacher he is! Gj mr woo
I think the more you know abstract algebra the better this video is
I wish i had a teacher like Eddie when I was in secondary school
Wish maths was taught like this when I was at school. I've paid more attention to this guy than four years of high school.
It's awesome that you're able to devote class time to so many fascinating topics outside the core curriculum. I've talked to high school teachers who say they're really constrained by the need to cover a mandated list of topics and prepare students for standardized tests. I'd be interested to hear how you navigate this issue.
I think it's extra classes, in which the students volunteer to do it.
Your videos gives me nostalgia and early morning high!
The way he plays with sets he's actually just talking about the cardinality of sets (which are actually numbers). So sets require (natural) numbers, and the basic blocks for those are the prime numbers.
My first instinct was indeed numbers, but then I thought it was 1, with everything being derived from the concept of 1. Then I thought it was definition (since 0 didn't seem to fit in with that) - using numbers to specify/understand something, like distance or an amount of time, and how they interact.
If only the history teacher I had was even half as good as he is...
The building blocks of mathematics are axioms by the way and numbers are symboles used to represent the cardinality of sets.
I would say the building block is logic because an axiom is something made true. Logic basically is true.
JustSaying 21 Logic is a tool in mathematics. You put in some axioms and use logic to build your mathematics from that. It's like axioms are the basic building blocks and logic is the fundamental forces
2:45
Mr. Woo: "division by zero"
Students: "YuSSSSS!"
earned a sub! its amazing how this was never explained in all my years of schooling
An atom is the smallest fragment of a given element. It can not be divided into smaller fragments of the same element. So the word still orks as a definition.
The sounds of the students when they finally understand, tell you, that Eddie Woo is an extraordinary teacher.
Almost got this right. The fundamental building block of numbers is proportions. Of actually all reality. It's a way of communicating/defining proportion. It's the language of Creation, and Creation is about differentiating the whole into parts.
A brilliant teacher. Thank you.
Zero is a good answer: all algorithms should start with the empty case as the base case; many design errors derive from failure to handle this!
My answer during the time when everyone else was shouting out: Logic
(I was juggling up between this answer and imagination - logic after all creates the orderly sequence of numbers that we know as positive integers and otherwise)
Will be interesting to see what the rest of the video shows haha great stuff :-)
I was thinking along similar lines. My answer: rules.
I think that too, in fact when you prove things you don't use sets. Especially proving mathematical logic and stuff. His title is not technically true since he wrote "all mathematics".
I would say logic must be applied to something for it to become math, so I wouldn't call it a building block. It's like the mortar rather than the brick. Of course you it's what allows you to build, but it's not the thing you're building with.
@@andrewprahst I would disagree, slightly. Logic is inherent. It need not be applied to something for that something to manifest naturally and systematically. Logic is what allows us to distinguish this from that, label and categorize them. You are correct in that logic isn't a building block - but it is the fundamental process that allows us to understand what the fundamental building block might be. To me, it's zero and I also consider zero = infinity.
Counting; or the need to count things.
Hahaha this is amazing you just got a student to ask themselves whether maths are real or not without realising it.
This guy is one seriously great teacher.
Hi Mr. Woo. You're right. There are many different origins of mathematics and science. For example, what's the basic building block of a computer. You start to tear it apart, and you find various circuit boards, such as the CPU (central processing unit), input, output, memory, storage, operating system, etc. There are building blocks of everything you see, such as computer software. If you dig deeper into it without using a scanner or an x-ray, you'll find binary code, which is the basic building block of computer software.
I wish we had more of these teachers, they help make learning fun and engaging. I would have loved to have him as my teacher👏👏👏👏👏
I thought the answer was axioms
Under the axioms would be computation.
onecommentaccount computation is also an axiom or a follow up of them.
Maybe? The incompleteness theorems show that infinite extension of the axioms can be insufficient for a problem, and I think corollaries of the axioms can have computational cost. Reduction to first order logic seems, to me, to be equivalent to the assumption that the total system never changes. I wonder if change is necessary to our existence; A perfectly reversible system can be used for perpetual motion! Such a system might exist, but I would not expect to find one available for experiment.
onecommentaccount I am a mathematician I know what I am talking about here
Neither of us needs to be accredited when we're just sharing our interest in the subject. If there's something wrong with what I'm saying, I'd love to hear about it.
I wish I had this guy as my teacher - his teachings on RSA encryption are the best I've seen
It's amazing high school kids have the opportunity to have a teacher like him lol. When I was in high school, our teacher was half asleep dragging through trig. This man is teaching his students things I didn't see until a fair way into university. Great guy tbh
My grandmother taught me about infinity when I was a toddler. So to me it made perfect sense. I had asked her what the biggest number was. She told me to guess and I said some number and she then said there was always a next number, forever. Blew my little mind.
What makes up Math? The equilibrium around numbers such as Pi, i, and e. Numbers are units we made up, but in the end it's just a balance of the numbers around equilibrium to come to an answer.
I think the basic building block of math is the concept of a whole, or one. Numbers arise when you need to keep track of more than one, operators arise when you start thinking of numbers abstractly, and new kinds of numbers arise when you start thinking of operators abstractly.
We were taught “Division by Zero is undefined!” Our teachers word! This was in 4th grade.
I hope I get to meet this guy one day...His brain's programmed to impart knowledge so effectively, systematically and logically to his students....using Logic!!!
Eddie im a young mathematician i really enjoy your way of teaching if possible i will like to attended one of your class
Number are just used to represent something. In binary system we use 1 and 0 to represent a particular no. We use diff permutation of combination of 0 and 1 to represent no.
14:35 "It starts with..." one thing, I don't know why. It doesn't even matter how hard you try... :P
I would say sets are the basic elements of mathematics. However, I think mathematics is about problem solving and modelling thing. And it is done by doing things with rules - algorithms. Creating more general rules and algorithms is a way of creating general models. It is one of the things what e.g. mathematicians do. And proving is the way of checking whether that model is good enough model.
Might even be able to say: just like we use words, we may use these other, names/words?, and put them together in different ways to say certain things? A possibility perhaps. Words are as empty, or, grammar structures are very much like algebraic variables, but more familiar to them.
Incredible teacher, I wish I had a teacher like him👏🏽👏🏽👏🏽
Oh, this reminds me of why i love mathematics so much!
Multiplication is the set of pairs of one item from the first set and one from the second. Division I haven't figured out yet.
Multiplication is the cloning of sets. Division is the merging of sets.
It's called Subitizing. After that, addition (combining sets) and multiplication (sets of sets). From there, we just make crap up as problems arise to remain consistent.
5:58 "I will explain it to you, but first ... some human sacrifices. Yeh, yeh! take these 2."
:)
@2:41 students go "yesssss" to learn Division by Zero. Love it!
I would have said the basic building blocks were "operations". Numbers and Sets are fundamental, but on their own they are just data. they're not information, they're not math. They are just values without context or use. It's only when they are being related to something that they contribute meaning. Operations might involve multiple numbers/values, but they are what create the context and meaning that makes math math.
Hell, even picturing "3" as presented here, as "the number of members of this set of three objects" is in itself an operation: equals/assignment. 3==[cup, cup, cup] for example.
Hey , Eddie , could u plz upload the full lecture of this part...??
I can not express how mind blown I am after watching this video . I discovering Eddie Woo's channel from a suggested video after 3brown1blue video that talked about group theory. Coming into this video thinking the basic building blocks of math being ratio's and portions(negatives are reflections and imaginary are laterals) gave me the understanding that dividing by 0 would take away the starting point or cancel out measurement (I thought of 3browns1blues linear scale).
I sat in my chair mind blown not knowing if I was peaking from the weed or actually having an epiphany. I thought dividing by 0 would create unmeasurable chaos. After watching his next video to find out why dividing by 0 is undefined I feel so inspired after this I feel i have direction and want to pursue a degree in math.
Wow! This video just gave me a profound philosophical amazement.
Buildung block of math: communications through symbols.
I personally always thought the basic building block of maths was 'definitions'. Because definitions of different terms used in mathematics are what set the boundaries that allow for the interpretation of mathematical rules & equations.
The definition of what a number is allow them to be used in a comprehensible manner.
The definition of a line allows for the existence of 2 dimensional & 3 dimensional shapes and the rules you can create in combination with the definition of lines & numbers is what is necesary for the creation of trigonometry.
My answer was counting.
Which is kinda correct, isn't it?
My answer too