The Axiom of Choice and Sets | #some2

The axiom of choice is a powerful tool and underlies a lot of mathematics. But what is this tool? How can we use it? And what do we need to do to get there?

Find out more in this video by Proffesional Math LLC!

#some2

[lexinwonderland]

Your animation is adorable and your overall video is fantastic but PLEASE work on your audio! I can barely hear some of the narrators even at max volume!

[HEHEHEIAMASUPAHSTARSAGA]

That's a good definition of ordered pair! I'd previously seen (a, b) := {{0, a}, {1, b}}, which also works, but it's a little harder to see that it works. {{a}, {a, b}} is simpler

[pl]

Love the humor in this one. Great style good content.

[xXJFARGAMERXx]

I wasn't really sure about it, but when you said it can reduce [problems] by 100% if you like and subscribe, I was convinced! So now I'm gonna like and subscribe (and dear viewer, why aren't _you_ subscribed and liked?)

[EulerWolf]

haha I was not expecting this style of intro at all.

[SunShine-xcdh]

If theres nothing in a collection is not a collection and not a set.

Cant the supposed empty set x≠x contain infinity since set theory itself is used to supposedly prove infinity doesn't always equal infinity.

[williamrutherford]

Some constructive criticism; you're using the medium of video, use it! Simply reading out the mathematical notation isn't very informative, either someone already recognizes the notation and will just read the text, or someone doesn't understand the notation and reading it out doesn't make it self evident. The fact that at one point you said "whatever THAT is" shows the core of the issue. Even if you get more comfortable with narrating, the narration itself needs to be structured like a sentence, not mathematical notation. Those little drawings you did for union and intersection? Do more things like that. Even just showing some examples would help people understand.

[niloymondal]

15:22 Isn't this circular reasoning? You are defining 'order' but you already assume the '<=' already works. Don't you have to define how '<=' works when comparing 2 sets?

Also, Axiom of Choice is a SCAM.

[nightspore]

Your cutesy little way of breezing through “explanations” at a speed no one who does not already understand the subject can follow is beyond annoying. I’ve studied the subject and still can’t keep up with parts of this unless I hit “pause” every few seconds. What exactly do you think you’re accomplishing? Is this just some lame attempt to show how off-handedly smart you are? If so, it ain’t working. Set theory at this level really isn’t all that hard, but it requires a reasonable degree of care and patience, two qualities conspicuously lacking in this presentation.