Axiom of Choice: Can you make infinitely many choices?

Zundamon challenges the mystery of the axiom of choice.

[BGM]

[Materials]
VOICEVOX:ずんだもん (Zundamon, illustrated by sakamoto_AHR)
VOICEVOX:四国めたん (Shikoku Metan, illustrated by sakamoto_AHR)
(+ other tools)
pixabay

This video uses synthesized voices.

#math

[fallensoulkun]

The third video for the axiom of choice this week... maybe I get it this time!

[dirtyduck]

Therapist: japanese Numberphile isn't real it can't hurt you

Japanese Numberphile:

[potato_fritters]

I love this channel, as an avid math lover. It doesn't just post simple/complex but common questions, but rather some thought-provoking math problems that always blow your mind.😊

[QuickCodeRL]

There is nothing more beautiful than a fresh video from Zundamon

[inverse_of_zero]

I'm a maths academic who did three mathematics degrees, including a Masters and a PhD. Whilst the level I currently teach is not that high, it is incredible to me that after over two decades in the industry, I can say that two anime girls on YouTube were the ones to finally get me to really understand the main gist of The Axiom of Choice. Phew... 😅

[Urbanxx]

I can’t believe you got me to watch a cute anime girl teaching math

[this_noetherian]

Happy maths foundation week videos (veritasium, up and atom, zundamon)

[RooiGevaar]

I secretly hoped that Zundamon would cover AC in their videos, as lots of YTbers made their own AC videos. 2025 is going to be the Axiom of Choice's year, LOL.

[artemis]

Damn everyone be making axiom of choice videos and I'm all here for it

[GenrGenc]

Axiom of Choice time! Let's assume that there is a uncountable set of videos about it constructed by choice from incountable class of sets of supreme math channels, so we can watch them

[Crispysyelloweyes]

Sorry but paradolia is making 1:20 too funny to concentrate.

[egg]

Idk how but this channel really makes math easy to understand

[SyuaibZulkarnain]

Why is Metan sounds like the king with speech impediment in Life of Brian

[PerriPaprikash]

after having watched the Veritasium video on axiom of choice, I thought i had understood the concept, but now after having watched this video, i have concluded that the axiom of choice cannot be understood.

[gavinlol-lopd]

I think that there is an alternative, more general way of proving each infinite set has a countable subset, and that is proving transfinite recursion based on the axiom of choice. Transfinite recursion allows you to choose an infinite number of times even when the set you're choosing from depends on the choices you made earlier. Then the proof becomes trivial; you can keep picking elements from the infinite set minus the set of elements you picked earlier.

[DanielBricefa]

These are adorable, and I hope they keep coming forever.

[SimonClarkstone]

My favourite statement equivalent to the axiom of choice: every connected graph has a spanning tree.

[ThisVan]

just watched a veritasium video on this topic a few hours ago and I was entirely hoping you had a video on it as well

[Nys]

Thank you Metan and Zundamon for providing these thought-provoking mathematics. The axiom of choice is indeed really strange, I believe it is used in the proof of the Banach-Tarski paradox?

[MikeRosoftJH]

Speaking about choices, choose one:
* A solid ball can be split into finitely many subsets (disjoint and non-empty), which can be moved around by translation and rotation, without overlap, to get two copies of the original solid ball.
* A solid ball can be split into more subsets (disjoint and non-empty) than it has points.