How about “every right triangle ratio explained.” I’ve had students whose minds are blown when they learn that there are more beyond sine/secant, cos/csc, tan/cot, etc…
I have always heard that the sets of numbers are like so: Natural: 1, 2, 3, 4... Whole: 0, 1, 2, 3... Integers: ...-3, -2, -1, 0, 1, 2, 3... Rational: All numbers p/q where p and q are integers with the exception that q can't be 0 Algebraic: Any number that can be defined in terms of addition, subtraction, multiplication, division, and roots of positive numbers ex. sqrt(2), phi (phi = (1+(sqrt(5))/2), etc. Or alternatively, any real number that is a solution to a polynomial equation Transcendental: Any number that isn't algebraic ex. pi, e, etc. Irrational: All algebraic numbers that aren't rational + the transcendental numbers Real: All rational and irrational numbers Complex: any number of the form a+bi where i is sqrt(-1) And of course there's extensions of the complex numbers to higher dimensions too such as quarternions and octonians, but those that I listed above are the major ones I've heard about.
As a Czech, the "Whole numbers" name makes sense to me! We call them "celá čísla", which translates to "whole numbers" in English ;) But I have programming in my high school, so I know what "integer" means too
The natural numbers were not "invented" any more than fire was. They existed before humans, but it needed humans to define the set. I like the fact that the number of ways of arranging zero things is one, rather than zero. Keep up the good work. I love maths 😊
I'm a professional mathematician, and I never knew until now that the phrase "whole numbers" is often considered to exclude negative integers. I always considered "whole number" and "integer" as exact synonyms. Okay, I've now looked on Wikipedia and found this: "The _whole numbers_ were synonymous with the integers up until the early 1950s. In the late 1950s, as part of the New Math movement, American elementary school teachers began teaching that _whole numbers_ referred to the natural numbers, excluding negative numbers, while _integer_ included the negative numbers. The _whole numbers_ remain ambiguous to the present day." So perhaps it's because I'm British rather than American that I've never heard of the use of the phrase "whole number" to exclude negative numbers.
Filipino here, and I've had the same idea in mind for years! I like to think that the naturals were named as such, because they were "naturally born out of the sense of counting", while the whole numbers implied "numbers that are "complete"", which can be interpreted as numbers without decimals. Of course, these are merely grammatical interpretations, and us mathematicians uncommonly use the term "whole number" to begin with.
Also the real numbers could be further partitioned into algebraic numbers like √2 and transcendental numbers like π. I guess it wasn't done because algebraic numbers are defined as a subset of real but also complex numbers.
8:01 "When we remove the 'Wholes' and the 'Rational' numbers..." No, those previously identified sets are *included* in the 'Real' numbers. The 'Reals' include the previous sets as subsets, so you do not "remove" them. Does the set of 'Real that are not Rational' numbers even have a name ?
The Real numbers that aren't Rational numbers are called "Irrational numbers". They don't have their own (generally agreed upon) symbol, so they are denoted by ℝ\ℚ.
What about quaternions? 3D complex numbers! Or I guess 4D if you count the real part. Or Dual numbers? Which are like complex but use e^2 = zero instead of i^2 = - 1.
I believe a more standard notation would use the Greek letter epsilon (ε): ε^2 = 0, ε ≠ 0. We were already using e for Euler's number, which is... a pretty important number, all things considered. (No worries if typing a Greek letter is inconvenient; you can simply spell the name epsilon.)
The H set (it's more like a subset but oh well) being the complex numbers with (R) real parts and (R+) imaginary part. In that case excluding number that have (R*-) imaginary part.
The video doesn't say that zero is nothing, only that it represents the concept of nothing. The word "nothing" also represents the concept of nothing, but it's definitely not nothing.
You should NEVER write uncountable set in a notation that lists a bunch of elements. Why does our journey end? Mention the fundamental theorem of algebra.
Depending on your definition, the set of natural numbers is not necessarily equivalent to the set of counting numbers. It's just that counting is how we started to develop an idea of natural numbers. In any case, I'm not so convinced by the idea that zero isn't a counting number. If you show someone an empty basket and ask them to count how many apples are in it, I think that zero is going to be the usual response, rather than, "That's impossible."
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Have suggestions for a future video? Leave a comment below! Thanks :)
Do hypercomplex numbers and their uses 🙏
Gregor Cantor and I would like you to do “every infinity explained”
How about “every right triangle ratio explained.” I’ve had students whose minds are blown when they learn that there are more beyond sine/secant, cos/csc, tan/cot, etc…
Every type of set theory, explained
@@themugwump33 You mean Georg Cantor?
Surprisingly high quality video for only having 100 views. Definitely gonna binge the rest of your channel!
"our journey has completed"
mathematicians with their quaternions:
This video is very well thought out and I hope to see more from you in the future :D
Bros a certified math major; love sky diving, reading history books and watching movies, then proceeds to make an all math channel
I have always heard that the sets of numbers are like so:
Natural: 1, 2, 3, 4...
Whole: 0, 1, 2, 3...
Integers: ...-3, -2, -1, 0, 1, 2, 3...
Rational: All numbers p/q where p and q are integers with the exception that q can't be 0
Algebraic: Any number that can be defined in terms of addition, subtraction, multiplication, division, and roots of positive numbers ex. sqrt(2), phi (phi = (1+(sqrt(5))/2), etc. Or alternatively, any real number that is a solution to a polynomial equation
Transcendental: Any number that isn't algebraic ex. pi, e, etc.
Irrational: All algebraic numbers that aren't rational + the transcendental numbers
Real: All rational and irrational numbers
Complex: any number of the form a+bi where i is sqrt(-1)
And of course there's extensions of the complex numbers to higher dimensions too such as quarternions and octonians, but those that I listed above are the major ones I've heard about.
In high school we were taught that, zero is part of a whole number system
Great video! I know it’s not really a set, but something on the surreals, or at least hyperreals, would be cool to see.
Great vid, keep up the good work!
Exciting !
As a Czech, the "Whole numbers" name makes sense to me! We call them "celá čísla", which translates to "whole numbers" in English ;)
But I have programming in my high school, so I know what "integer" means too
Fascinating!
Gregor Cantor and I would like you to do “every infinity explained”
tetration is repeated exponation so if we make it like square roots the what will be the tetrated root of i
There is still other sets such as Quaternions, Octonions, Sedenions, Pathions, Roudons, Chingons and Voudons
Those sound like alien species
The natural numbers were not "invented" any more than fire was. They existed before humans, but it needed humans to define the set. I like the fact that the number of ways of arranging zero things is one, rather than zero. Keep up the good work. I love maths 😊
I think there is a "raging" debate in philosophy of mathematics about whether math is discovered or invented. I can see the case for either/or.
That's true bro
@@brenatevi In my view, we invent the constructs of mathematics and discover the sensible ones.
@isavenewspapers8890 This is a good take
@@ccbgaming6994 Thanks!
I'm a professional mathematician, and I never knew until now that the phrase "whole numbers" is often considered to exclude negative integers. I always considered "whole number" and "integer" as exact synonyms.
Okay, I've now looked on Wikipedia and found this:
"The _whole numbers_ were synonymous with the integers up until the early 1950s. In the late 1950s, as part of the New Math movement, American elementary school teachers began teaching that _whole numbers_ referred to the natural numbers, excluding negative numbers, while _integer_ included the negative numbers. The _whole numbers_ remain ambiguous to the present day."
So perhaps it's because I'm British rather than American that I've never heard of the use of the phrase "whole number" to exclude negative numbers.
Same here in Romania, the term for integer literally translates to "whole number".
Filipino here, and I've had the same idea in mind for years! I like to think that the naturals were named as such, because they were "naturally born out of the sense of counting", while the whole numbers implied "numbers that are "complete"", which can be interpreted as numbers without decimals. Of course, these are merely grammatical interpretations, and us mathematicians uncommonly use the term "whole number" to begin with.
No Quaternions etc. not every number..
No one is gonna put all number systems in one video
Also the real numbers could be further partitioned into algebraic numbers like √2 and transcendental numbers like π. I guess it wasn't done because algebraic numbers are defined as a subset of real but also complex numbers.
Your "etc." is quite significant. 🙂
For real, bro. No sedenions and octonions either.
we really need to make a set called the set of numbers
8:01 "When we remove the 'Wholes' and the 'Rational' numbers..." No, those previously identified sets are *included* in the 'Real' numbers.
The 'Reals' include the previous sets as subsets, so you do not "remove" them.
Does the set of 'Real that are not Rational' numbers even have a name ?
irrational numbers
The Real numbers that aren't Rational numbers are called "Irrational numbers". They don't have their own (generally agreed upon) symbol, so they are denoted by ℝ\ℚ.
He said: "When we remove the 'holes' in the rational numbers".
As for your second question, yes.
They are called the "Irrationals".
@ You're right. Thank you.
What about quaternions? 3D complex numbers! Or I guess 4D if you count the real part.
Or Dual numbers? Which are like complex but use e^2 = zero instead of i^2 = - 1.
I believe a more standard notation would use the Greek letter epsilon (ε): ε^2 = 0, ε ≠ 0. We were already using e for Euler's number, which is... a pretty important number, all things considered. (No worries if typing a Greek letter is inconvenient; you can simply spell the name epsilon.)
Z is named after the German word for numbers bc they have been invented/discovered by the Prussian/German mathematician David Hilbert
❤. So so amazing. In the future, whole Set will be their father?!😄
E os quatérnions? E os octônicos?
Where is H :(
what is H?
Well it is like P, a subset of another set....
V☠
@ quaternions
Any reason why this is broken into two lines?? 2:32
Ah, yes, that is odd.
3:53 That could be onto a video itself
What about every other field extension of Q? hehe
Quaternions, Dual numbers, Octonions
The H set (it's more like a subset but oh well) being the complex numbers with (R) real parts and (R+) imaginary part. In that case excluding number that have (R*-) imaginary part.
Good video but why the music?????
I love the fact that there's pleasant music in the background in these videos.
Same @@DrJulianNewmansChannel
Copyright friendly, I suppose
Natural numbers=whole numbers on the positive side of the number line
isnt 0 part of whole numbers not natural?
1:11
@@isavenewspapers8890 oh, our country includs n + 0 as whole number
Early button ❤>>>>>>>>
and it goes on and on, and i would've been interested in anything but what was presented :)
The number zero is the empty set, whose existence needs to stated as an axiom. It is not nothing.
The video doesn't say that zero is nothing, only that it represents the concept of nothing. The word "nothing" also represents the concept of nothing, but it's definitely not nothing.
Uhm he forgot abt the quatornians and beyond
You forgot exponentiation.
Does anyone else read fan fiction while listening to math videos
You should NEVER write uncountable set in a notation that lists a bunch of elements.
Why does our journey end? Mention the fundamental theorem of algebra.
Zero is not a natural number, you don't use 0 in counting (which we do −the counting− in nature)
Depending on your definition, the set of natural numbers is not necessarily equivalent to the set of counting numbers. It's just that counting is how we started to develop an idea of natural numbers.
In any case, I'm not so convinced by the idea that zero isn't a counting number. If you show someone an empty basket and ask them to count how many apples are in it, I think that zero is going to be the usual response, rather than, "That's impossible."