The Axiom Behind Math's Weirdest Paradox

Comments · 173

• AB

  @AbideByReason · 5 months ago · pinned

  Join my Patreon community: <a href="https://www.patreon.com/abidebyreason">https://www.patreon.com/abidebyreason</a>

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• DO

  @douglasstrother6584 · 1 year ago

  It&apos;s fascinating how the simple act of counting transforms from a very intuitive act to the boundaries of Mathematics.

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• US

  @user-sl6gn1ss8p · 1 year ago

  So maybe I&apos;m a little drunk but I was hoping for more meat on the axiom of choice, what it means, why is it deemed necessary, and how it leads / is involved with with unmeasurable sets.<br><br>That being said, great video - I really like the visuals : )

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• DR

  @DrMcCrady · 1 year ago

  Your sphere animation is really cool!

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• YA

  @yanntal954 · 1 year ago

  I just want to point out that you don&apos;t even need the full power of choice to prove unmeasurable sets and Banach Tarski.<br>In fact, Hahn Banach lemma is enough to show paradoxical subsets in S^2!

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• PO

  @powderedphantom5765 · 1 year ago

  Weirdly high quality for the channel size. I appreciate it, hope you’re channel gets the recognition it deserves

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• RA

  @RalphDratman · 1 month ago

  This is excellent: clear and very informative. Thank you!

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• HA

  @hahahasan · 1 year ago

  Fascinating

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• HE

  @henrikljungstrand2036 · 1 year ago

  The problem is not the axiom of choice per se (when properly formulated). The problem is classical (non-constructive) logic, especially when applied to infinite sets (i.e. monotonically growing sets, generated by unbounded, infinite procedures). The halting problem is a real mathematical problem, and cannot be &quot;spirited away&quot; without due consequences. It is meaningless to claim any proposition to be true or false unless you know what it claims constructively, and know how to prove or disprove it constructively. Semantics is usually more important than syntax, and the logical rules of syntax should be adjusted so that it is always semantically meaningful. Even &quot;Platonic ideas&quot; are always material (thought) constructs (of consciousness!) that must be created constructively in order to exist, there is no such thing as truth without construction or reflection.

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• VA

  @VaraNiN · 1 year ago

  Great video and awesome animations! Subscribed!

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• BO

  @Bolpat · 1 year ago

  I wouldn&apos;t describe Georg Cantor as “Russian-born” not because it&apos;s false (he was born in St. Petersburg), but because it&apos;s misleading. Cantor was German. His name is German and he published in German, and lived most of his life in Germany.

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• PU

  @PunmasterSTP · 1 year ago

  That diagonalization argument is so cool!

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