Відео

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...

Clark James Williams Kenneth Robinson Anthony

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^+

The questions are giving me Vsauce vibes I love it

As someone who is familiar with programming and have mild experience with Agda, this was delightful to watch! It seems like everything up to your definition of the integers is fairly standard in Agda, but the way you defined the integers isn’t. (It seems more directly related to how they are defined in cubical Agda, or at least 1Lab.)

7:31 the (k+1) should entirely be the power of 2. But the result is still correct. Nice work.

This is amazing.

Every time you cut from the animations in front of a dark background to yourself in front of a white wall, I felt like I was getting flash banged and that ruined the flow of the video. Please try to avoid such drastic changes in brightness in future videos!

24:48 I think at the end of the first row it should say [(ad+bc, bd)]E. Great video!

I think I also read somewhere that AC is equivalent to Lagrange’s Theorem from group theory; specifically, the generalization to infinite groups. For this one, it’s actually easy to show AC implies LT, but harder to show LT implies AC.

Really nice overview of the motivation for being rigorous! Can you recommend a book or article to read up details? Especially about the step to the real numbers.

at 32:52 , when presenting the dedekind cut for a rational, it's defined as `q < r`; does that imply that r itself isn't in the set defining Q? I feel it should be <= intuitively. also, is it possible to two irrationals without a rational between them? that would imply that there's reals with identical representations though, so I guess not by definition? I guess I'm pretty confused on how irrationals are represented, but that's a kernel for reading great video, thanks!

I was literally searching for this yesterday and I found almost nothing. Thx mate.

@19:45 wouldn’t showing this is a transitive relation use subtraction? But that’s not an operation we have yet. We would have that (a,b)~(c,d)~(e,f) Then a+d=b+c c+f=d+e We want to show a+f=b+e So we can add the two equations to get a+d+c+f=b+c+d+e Then by canceling the d+c on both sides we get that a+f=b+e, hence (a,b)~(e,f). But the step of canceling the d+c term uses subtraction which we don’t have yet, so I’m unsure about that.

@16:20 we would need a negative in front for negative real number though.

Mate I love your channel, it's criminally underrated. It's clear you have a real passion for mathematics. I graduated with a bachelors in Mathematics 4 years ago and I missed topics like these, we did a bit of set theory but never into the nitty-gritty like this. Would you ever consider doing a video of other constructions of the natural numbers like Peano axioms? Either way, love your content!

great, to say there's nothing is to be god. in the beginning there is nothing, and then god create 0, there there is nothing and 0. and from that all math and universe created. hahaha

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jHan is awesome. And handsome. But "is zero a natural number?"? Man ... the answer to that is very simple: each person decides ... it is a matter of convention. If you want to consider zero a natural number, ok. If you don't consider zero a natural, that's also ok. THAT'S the answer. There is nothing more to it. I don't understand why people still ask such question ...

I liked this presentation, but I feel like the last 30 seconds suddenly brought up some controversial claims with no backing. "Set theory isn't a painstaking formalization for the sake of formalization" I feel like that was why Set Theory was created, though that's certainly not what modern Set theorists do. "The axioms, theorems, and tools of Set theory have applications in every branch of mathematics" I feel like, with the possible exception of the Axiom of Choice, the axioms intentionally don't have applications. They're just a foundation from which we can get things the rest of math needs, like the fundamental property of the ordered pair. And the theorems and tools of Set theory, like forcing and the results that come from it, have essentially no bearing on other fields of mathematics. To be clear, I enjoyed my graduate Set theory classes and I like formalization! I just don't see things the same way.

I subscribed literally today and you uploaded a new vid already awesome

very clear thank you so much 🤩

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Beautifully explained, connecting all the dots reaching the eureka moment. Thank you so much. Have subscribed to your channel immediately 😁

Great video !

Thank you

You didn't really explain what sets are very well, no offense. For example, at 4:55 (a,b) != (b,a) "a,b are not the same if b,a are not the same". This is very difficult to understand from the perspective of someone who doesn't know set theory. a and b are the same by virtue of the fact that they're a and b, so how can you say they're not the same? it's like saying: (1, 0) != (0, 1), "1,0 are not the same if 0,1 are not the same". What? And then your second example, (a,b) = (a', b') if and only if a=a' and b=b'. That's like saying 1=3*1 and 2=3*2. What? This left me no where closer to understanding set theory.

You’re doing great! Keep up the good work!

But does that mean all lines are equal? Because we can define a one to one correspondence for any two lines . Or we shouldn't related something that is physical to something that is human made( i.e points) I mean we shouldn't say that just because two lengths have the same no. Of points that mean they have same length? Isn't it a paradox I am very confused. If I take the length as an infinite set of points and we can show that all lines have same no. Of points so that means all lengths should be equal?

Look at my quant!

My name is also pronounced J-Han and I also make math UA-cam videos so what a weird coincidence. This is a great video. You are an excellent educator!

First time for me that someone described it so simply and obviously.