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Cool video, very informative and clear

If the two jars are separated in space, they are differently located.

awesome topic

Greaaat

I like this channel

Great! I love your revisualizations at the end. To see such structure emerging in the simple act of counting.... Quibble: at 6:26: you define the "<" relation as the proper subset relation, but this is not correct without qualification, since there are many subsets of an ordinal that are not ordinals at all. The more natural relation (which is part of what makes von Neumann ordinals so cool) is simple set-membership: x<y iff x is a member of y. Then you wouldn't need to qualify "x is an ordinal" -- and in an introduction like this you surely wouldn't want to: the whole point is to show how ordinals ordinals to "emerge" (almost by magic!) from the recursive A-union={A} operation. One other thing: you write "si" for 'if" there, which makes me happy but might confuse some people! 🙂)

how do you find the 6 first numbers ? That is the interesting problem.

Green Track

axiom is what we can't do any better

Tremaine Roads

Your videos helped so much! But can you please share axioms 7,8 and 9 too?😢

You are making simple things complicated.

Please try to put the shape alone in the picture when u ask us to pause.

1st is Axiom of Extension. Halmos, Naive Set Theory.

Fantastic video! I've been self studying set theory and was having trouble understanding the notation for this axiom, but this video cleared it up fantastically. Thank you!

Nice solution

why was i tagged?

The barber shaves all men who do not shave himself. Who shaves the Barber?

Thank you, Professor. Will you make the video for axioms 7,8, and 9?

Chau

Nice intro dude 😂

Women do shave

Meh, 7 segments is nice and easy, no need to do 4

I find in many cases 6 segments is the lower bound for making the digits normal. It would also be the minimum for display all 26 letter and numbers distinctly in one case. 6 is just enough segments to display all in capital and lowercase as well as numbers, but a lot of 7-segment displays don’t have support for an M or W. Hence why 14 and 16-segment displays have become so common.

I don't understand what you mean by quarter circle? But the ant will turn 5 times (R,L,RL,R) before it gets back to A.

It's the Fibonacci numbers

It's ( 2n^3 + 5n^2 + n )/8 1^2+2^2+3^2+...+(n-1)^2+n^2 - [ (1^2)/4+(2^2)/4+(3^2)/4+...+((n-1)^2)/4 ] n^2 + SUM i=1 to n-1:(i^2) - 1/4*SUM i=1 to n-1:(i^2) n^2 + 3/4*SUM i=1 to n-1:(i^2) n^2 + 3/4*[ SUM i=1 to n:(i^2) - n^2 ] n^2 - 3/4*n^2 + 3/4*SUM i=1 to n:(i^2) 1/4*n^2 + 3/4*[ n*(n+1)*(2n+1)/6 ] 1/4*n^2 + 3/24*[ n*(n+1)*(2n+1) ] 2/8*n^2 + 1/8*[ n*(n+1)*(2n+1) ] 2/8*n^2 + 1/8*[ 2n^3 + 3n^2 + n ] ( 2n^3 + 5n^2 + n )/8

b^0=1, because the right limit and the left limit are equal to 1 for all positive non-zero base value in R.

But is congruence identical to equality?

U Look Like Clever 😜😺

Maybe worth noting that there are non-classical, paraconsistent logics within which derivations of the sort you sketched (say, of 1=2 from an arbitrary contradiction) don't work. For example, in typical relevant logics, disjunctive syllogism is not valid.

I think it's kinda misleading to equate the special case with the axiom itself.

I understand the point of your videos. Still, I don't agree with them in terms of foundations upon which we can start building up maths. Indeed, to formulate those axioms we need something even more fundamental that we need to agree on : first order logic. You couldn't even formulate your first axioms without the "if and only if". It is so simple that it is taken for granted but it shouldn't because there I so much logic that intuition alone can provide. Hence the difference between logic and common sense. Once implication is involved, things start to become messy and without that knowledge, building up maths will quickly become a dead end. But yeah, I understand the simplification here since it's hard to start with logic without knowing a thing about sets and axioms and it's hard to introduce sets and axioms without knowing logic. I firmly believe those 3 should be taught in parallel but to grab people's interest, it's a cool place to start.

6:50 “An axiom is something that does not need a proof“ 😂😂😂😂😂 no. And axiom is a ground truth by definition. Meaning we say that it’s true. Or we assume that it’s true. And then we build the rest of our system on this and other assumptions. Its truth is assumed by definition. We might be able to prove it we might not. We just assume for now that it is true.

I love this and I find it hilarious 💀

Don't forget Terrence Howard's axiom that states : 1x1 = 2

How successful social behavior like curses and blessings becomes addition and subtraction into marketplace is amazing and telling in ways I can't believe it took so long to learn ourselves and how we Triangulate readability and judge thermodynamical systems with legibility. A truly amazing interactive measure. The keys to the cosmos textualism methodology objectivism truly separated us from ancient world bumbling around with shared knowledge just no way to doing anything with it.

thanks! I love the step by step!

For Terrence Howard, the most important axiome is 1x1=2

Well, if you don’t like it, you just define a solution out of the blue. Haha, that’s maths.

I always heard you can prove anything from a contradictory statement, but never seen the actual construction. Nice

Respect!

These are very amusing videos, and I think you might be on to something! Two suggestions: 1. I'm not sure you should call set-theoretic axioms "_the_ axioms of math." You can "start" math in any number of ways, and even if you do start with set theory, there are different axiomatizations that will do the trick. 2. The way the Axiom of Foundation is often formulated (in contrast to your depiction and the basic intuition of banning infinite regress) is very hard to understand ("there is an element of the set that shares no member with the set "); maybe you could do a video on how it works? It might be too advanced for your intended audience; I don't know.

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✅🧡👍🙏

Is there a standard "canonical" set of axioms you're going with for this series? I know that in most axiomatic systems, one can often interchange some of the axioms with some of the most basic theorems and get an equivalent axiomatic system, so how do you decide which basic things you're going to call axioms in this series? For example, I notice you have the axiom of choice as axiom #9, but as I understand it, you could have chosen Zorn's lemma instead for that one.

Really cool solution :D

Sorry, I'm allergic to thumbnails with open mouths.

The lilies will account for half the pond on the 99th day. I like how several of your proofs in the video kinda work backward. That seems to be an easy way to think about the lilies, too. So, from now on, I'll try to remember to look at any problem I want to solve, and maybe consider it in reverse, or backward.