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When you multiply 0.33333... by 3, and the result is 0.99999..., this doesn't show that 0.99999... is equal to 1. It shows that the exact real answer to the 1/3 operation is not 0.33333..., it's just an approximation. By definition of division, if you divide A by B and the answer is C, then when C is multiplied by B the result must be A. If the result is something different from A, answer C to the A/B division is approximate, not real.

Zero is even because is simply zero

i is like dark matter. every video like this keeps saying imaginary numbers are rock solid and stuff.. but nobody knows anything about them, they just use them and know how to work with them. battered housewives would find this familiar. what are the digits of i ? does i even have digits? numbers have all sort of properties. i doesn't fit in with near-anything you can say about any given natural number. you can't even say complex numbers are just a pair of real numbers because i shows itself in real number operations. same with irrational numbers. we know how to get some and can use them but they're very much beyond the imagination for the most part; so far.

Thank you for this video. Very cool puzzle

Sir, I don't know if you will ever see this, but i want you to know that you are one of the best internet teachers i have ever come across. Thank you for explaining everything so nicely.

I'd argue that 0 has even properties, but it's properties are too exotic to be lumped in with the even numbers. For instance, I can divide by any arbitrary odd number I like, but I can't divide by any arbitrary even number unless I explicitly exclude 0. Your reason 5 proof by contradiction only holds if all integers must be either even or odd, but why can't the definition be that any non-zero integers must be even or odd. Your reason 10 is an argument against 0 being even since infinity is not a value and fits more with the idea that 0 is a multiplicative mask rather than an even number.

i love this man's video, it feelslke like cleaning my room

delicious

8th reason isn't that good of a reason since you can argue the same with 0 being odd for group of odd integers

Reason 5 is the best reason; there is no integer solution to 0 = 2n + 1. We all agree that 0 is an integer, and since 0 is not odd, then it has to be even. This proof is decisive and *must* be true.

7:40 If someone tells you that 0 is not even, let them know that it would be odd

Of course 0 is even, I can divide my zero quantity into two zeroes 😅

0 is even because it can be written as 2k with k being an integer. That‘s all, the definition of even numbers. All the other reasons follow from the property of an even number because by definition of even numbers 0 is even.

I thought about this in Year 2 and explained into to my teacher, she said I was smart and I never forgot it: Odd + Odd = Even Even + Odd = Odd Even + Even = Even 1 + 0 = 1 Considering "1 is odd", the equation is either: Odd + Even or Odd + Odd. Since 1 + 0 = 1 and 1 is odd, therefore we have: Odd + Even = Odd. Therefore, 0 is Even.

I remember in first grade learning this and was confused, they never taught us integers, so when they asked if 3 was even, I said yes, it has two even halves each being 1.5. 15 minutes later they said it could not have a decimal and I finally understood

4:19 What would happen if the ray intersected the polygon at a single point? Would the point be in the polygon? Also, can it be any infinite point, from any direction?

I don't get it, why would anyone think 0 is not even in the first place. this whole debate should not have happened at all. This whole video would look the same if you replaced all zeros with twos. all the arguments are the same. let's discuss 10 reasons why 213423 is odd. there's literally nothing special about 0, 2 or whatever other integers.

Zero is even and an even threeven number.

I love the second one. Gonna use that explanation for my middle school students!

All this is very true, but there is always that One Big Question about the special numbers and constants such as i, e, pi, etc., and that is they seem to be necessary for our structured reality to exist, but why? Why do all the ratios and integrals and probabilities exist the way they are? Did we invent them, discover them, or did the Cosmic Mathematician design them? Inquiring former math majors would like to know. I'm 81 and would like an answer soonest!

clean editing, nice script, liked.

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for the mobius function, why are multiples of squares defined to be 0? doesn't that just break the multiplicative property? e.g. mu(4) = 0 != mu(2)*mu(2) = 1. if we just counted all prime factors (with multiplicity), it would be multiplicative for all numbers, not just coprime ones

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The most obvious reason is that it’s between two odd numbers

Nothing "is" anything. Neither the objects nor the categories exists. It simply makes sense to categorize certain things with certain other things: like zero with "the even numbers".

7:37 ν₂(0) = ∞! = ∞ yup, checks out :D

11: Zero is even because the last bit in its binary representation is zero

0:07 of all the answers given there, "even" is obviously the best answer but the second-best answer is woefully underrepresented: "I don't know."

I haven't watched it yet, but I can only expect an incredible video as always

Call me mad but e=π=3 g=10

As a physics major, is there a level 0?

give me extra e-2!

let say "i" exist I prefer imaginary in geometry than in algebra though because in algebra "i" kinda feel dry

If lim_{t -> 0⁺} 1/e^{t/t} = 1/e, then you’re saying 0^0 = 1, which is the same thing we get from the other limit.

does math equal reality?

When we got to level 4, I literally shouted out “Limits!” I learnt a tiny estimation when I was in precalc class as a sophomore.

These cookies at the beginning are so ugly

Nice Video, though it should be obvious that if you have no nothing, you have something. That is the reason of our existence, isn't it?

Sometimes even math-nerds do too much pot.

I can't do it by math, but phylosophic it is the same as before, cuz you divide something by nothing, kinda not, kinda don't. So it's the same.

If you have 6 cookies and divide by 0 friends, you still have 6 cookies. 🤷‍♂️

In Level 4: If "there should be a gap", how can they be equal? 🤔

Beautiful exposition with just the right dose/exposure of a new topic.

This guy looks like a teenager or younger, or is it that I am getting so old at -> 62 lol😆🤣😆, anyway very good can't fault you in anything I have seen so far

thank u so much i really love thsi video and i just subscribe u keep making such videos.thank u so much

"The lebesgue integral is usually only seen in grad school"??? What

math major would just set e=exp(1)

1:32 if my friend already has some debts and I am removing it then it must result in zero. How it is positive??? 😅😂😂

The following three articles explain that every number is divisible by zero. In doing so, they refute the claims in this video. I recommend reading these articles if you want to learn division by zero from different perspectives. 1.Division by zero in the light of the five fundamental principles - Beş temel ilkenin ışığında sıfıra bölme 2.A study to prove that the denominator can be zero in fractional numbers - Kesirli sayılarda paydanın sıfır olabileceğini kanıtlamaya yönelik bir çalışma 3.The problems created by zero in the division operation, their reasons and an attempt at a solution - Sıfırın bölme işleminde oluşturduğu; sorunlar, nedenleri ve çözüme yönelik bir deneme çalışması