Відео

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!

4:00 technically there has to be none leftover in the codomain, not the image of f

The best statement of AC I've come across is: Let S be a set of nonempty sets. Then the Cartesian product of (all) the sets in S is nonempty. Of course this statement implies that such a Cartesian product exists, but otherwise it seems totally obvious, and feels a lot clearer than any description of choice functions or choice sets. 😊

I wonder the cardinality of the complex numbers set (that set is also not ordinable like the real numbers set).

how can an axiom follow from something?

Very good explanations! You might have spelled out what "two to the power of aleph one" was; that had my audience slightly confused. My only complaint is the music, especially in the middle: dreary and unpleasantly atonal, including a weird "chchcht" noise that with my headphones on gave me the feeling something was being sprayed up the middle of my nose...

How didn't I know about this channel earlier? The world needs to know about the channel.

Maybe it's just me, but I find the music very distracting. 10/10 for all the rest.

Fantastic video

Love the video! I do have one small criticism wholly unrelated to the mathematics: the background music is too loud to the point that it gets a bit overwhelming when wearing headphones. Everything else was pretty much perfect.

beautifully explained

0.011111...and 0.1 is actually the same number in binary, its like 0.999...=1, since the difference should be small enough to be 0, hence the same number🙃

Basic and unforgiveable mistakes? Set theory defines numerals as numbers, otherwise there are no sets or combinations. A set is a heiroglyph or picture of objects that look like mathematical symbols. The properties of the members within the heiroglyph are not transferred onto the set or heiroglyph. The stand-alone iconic form of a number is, and is called, a numeral. A numeral is void of a mathematical container, application or calculus, and a collection of them must be significant for it to be called a set or collection, for example a set of cutlery is significant because it is a tool. Numbers are not transferable between applications, and are themselves void, and not countable, existing only in their calculus. The introduction of infinity into set talking points is an attempt to place the first non-number into a count, usually placed at "the end" because it has no stop - numbers are created through a stop. The largest number is the last stop in the count, such as 6, or 13. Mathematicians will disagree. Mathematicians do not like philosophers.

mileswmathis.com/nash.pdf

r u contributing to the advancement of PROPAGANDA? A lil dramatic. How many have been lost to history? TODAY a MATH & SCIENCE genius is CENSORED & completely ignored by the fraud that is mainstream math & science. Miles W Mathis.

Great job brother ❤

A am a mathematican my name its banmien 15 years a am creat new math name math its a black mathematics and very good theory

This channel will have a bright future

Really good animation!

Weirdly enough, this doesn’t sound like an axiom at all (even though it is called one). Kinda like Euclid’s 5th postulate.

thank you so much 🤩🤩🤩. much better than class

Excellent video !!!! Perfect explanations. Nice !!

11:51 That should be A(m,1) = A(m,0)^+ = m^+