วีดีโอ

The comtinuum is 1. A single unit. 1 + 1 + 1 + 1 + 1... = 1 = N = R. Numbers have relative values, they are ratios of an single unit. 1 + 1 + 1 + 1 = 4. Each 1 have a value of 1/4, 1 € N. N = R = C in 1. This because every real number can be expressed as an inverse of 1 times an multiple of 1. 0.5 x 2= 1, 0.25 x 4= 1. Every number can be expresed as an ratio of 1. That means 2 is 2/1 when the value of the 2 individual units is 1/2. Natural and real numbers have relative values. Numbers come from a single UNIT.

The cyclical nature of these functions is beautiful. If you’ve ever done an integration by parts problem with a trig function it’ll start to cycle if you don’t stop it early. Also the way I remember derivatives and integrals of sin and cos is with four quadrants. sin -cos cos -sin If you move clockwise on the wheel it gives you the derivative. If you move counterclockwise, the integral

Awesome video!

Amazing video on the topic.

Mmmrrmm yesss the nOnEmPtY set has eLeMeNtS that i can pick!!

You are doing a great job unpacking so much in this video. I need to watch it again to absorb more if it.

big W for your vid and yt career, you remind me of vsause but more formal but still introductionary like him, im studying math rn and this vid is actually good quality

that's amazing

The problem I have with the diagonal method is that the same method can be used to show any partial set of whole numbers is incomplete.

Zorns Lemma

Excellent breakdown and video here. also/and the outro commentary of these concepts - master class. ty

This video was amazing!

realy good vidéo, thank you

We would like to know more about Yutaka Taniyama

means e^-1 =-1 is wrong and π must=0

How many degrees is X?🤔

0=(0,0)

cos(0)+isin(0)=0 but it isn't equal really 0

Background noise (drum) is very annoying.

That was magical...simple and elegant!

Music on the background is very disturbing

an axiom that does crazy stuff

Euler and Guass were the greatest mathematicians to ever live respective to their time

Thank you for this video! I understand the AoC much better after watching it. It's fascinating to see how thoroughly set theory is connected with other branches of mathematics. The visuals and audio were fantastic, and you explained things at exactly the right level for me (2nd year undergrad). I feel like I've just watched a very strong lecture at my university. Subscribed :)

4:22 Bernays

talk tuah

poopy fart head

i spent a day trying to prove this with the taylor series, still my most enjoyable day in terms of math

Amazing video, Physics major and we use this all the time, now I have a much more intuitive understanding of the Euler's formula

I am familiar with Dedekind Cut a few years back. But this is the first time I learned the rationale behind the rationals.

A whole series of videos of ZFC like this will surely go viral.

2^136279841-1, new largest known prime, discovered Oct 12 2024

In a university study you would expect a more precise language. You would hear Euclid's proof explained as "there are infinitely many primes", as in, not just finitely many primes. Rather than "there is an infinite number of primes", easily misunderstood as if to say there is a certain number of primes, and that number is infinite. This only becomes meaningful once you also realize that there is a set the elements of which are exactly the primes, and this set has a certain cardinality, and that cardinality is infinite.

Thanks! This really helped

im gonna try and find the biggest perfect number i can fathom Day 1: 137438691328

I started gasping and lighting screaming when i saw the end of the taylor series proof. Im bewildered

I love this

Great video, it's so hard to find maths content that isnt either not related to what you want to find or just incredibly complicated.

This video is pointless since euler formula is simply wrong. Left side is exp function which ranges from 1 to infinity. Right side is the sum of 2 trig functions each ranging from -1 to 1. So, how can these sides ever be equal? Stop parotting, start thinking.

what's your book there?

You deserve more subscribers, amazing explanation loved it.

The game.

amazing man! subscribed

22:50 I almost immediately think, why can't the reals be ordered like you do with the integers? Compare the absolutes of two numbers, and give the priority to the positive should their absolutes be equal. Unless of course, you are talking about Dedekind cuts.

Thanks for the video really helpful for my university class.

This is a perfect video! I just have one question: why is natural number to the power of natural number the set of all positive integer functions? Can someone please explain it for me😢

Ratke Spurs

Amazing video but I still have one question. Like how do you classify e^ix as imaginary or real? Like for imaginary i must be multiplied to the number and for real no i at all. But this e^ix has i in the exponent, so I got confused at this part.

14:46 wouldn't the domain be a subset of the power set of X? if x belongs to a particular Xy_1 it cant belong to any other such Xy_2 so the domain would be like disjoint subsets of X?

17:00 The musical choice is fantastic! It truly whisper the idea of "there's some powerful concept here to be grasped, but it's doomed indeed". Genius! Also, the part immediately preceding it has got a VERY inspiring music, which lift the spirit to the idea of "this concept is very powerful, harnessing the power and patience of infinity to gain the ability to be exact"! (17:00 _unless_ ... *there's a hole** ) also, the ending speech and the "almost pun" is ... delightful! I love it!