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HoldMyTypeMath's Strangest Set Vitali and <a href="https://mathstodon.xyz/tags/axiomofchoice" class="mention hashtag" rel="nofollow noopener" target="_blank">#axiomofchoice</a> <a href="https://youtube.com/watch?v=hs3eDa3_DzU" rel="nofollow noopener" translate="no" target="_blank">https://youtube.com/watch?v=hs3eDa3_DzU</a>

Mark T. TomczakI think, for the first time, I ran organically into a situation where the Axiom of Choice helped me reason through a mathematical quandary. Shout-out to my math acquaintances to help check my reasoning.So here's the question: can you choose a random real number? More formally: on what basis do we logically conclude that every real number is a viable candidate for random selection if you are selecting a random real number?The reason this is even a question is that the definable reals are a subset of the real numbers; not every real number can even be named using a finite description. So the question arises: can you pick a number you can't even name?And unless I've missed something, I think the Axiom of Choice says "yes." Real numbers can be described with an infinite sequence of digits (before and after the decimal), each digit is chosen from the finite set 0-9, we accept without chasing the evidentiary chain that you can randomly choose one element from a 10-element set, and the Axiom of Choice asserts you can therefore construct a real number's representation (an infinite set) by choosing a random element from every 0-9 option in both directions (two infinite sets).This works, yeah?<a href="https://mastodon.fixermark.com/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mastodon.fixermark.com/tags/AxiomOfChoice" class="mention hashtag" rel="nofollow noopener" target="_blank">#AxiomOfChoice</a>

M. Ní SídachThe Man Who Almost Broke Math (And Himself...) <a href="https://sfba.social/tags/Veritasium" class="mention hashtag" rel="nofollow noopener" target="_blank">#Veritasium</a> <a href="https://sfba.social/tags/DerekMuller" class="mention hashtag" rel="nofollow noopener" target="_blank">#DerekMuller</a> <a href="https://sfba.social/tags/VideoEssay" class="mention hashtag" rel="nofollow noopener" target="_blank">#VideoEssay</a> <a href="https://sfba.social/tags/History" class="mention hashtag" rel="nofollow noopener" target="_blank">#History</a> <a href="https://sfba.social/tags/Culture" class="mention hashtag" rel="nofollow noopener" target="_blank">#Culture</a> <a href="https://sfba.social/tags/Science" class="mention hashtag" rel="nofollow noopener" target="_blank">#Science</a> <a href="https://sfba.social/tags/ArtScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#ArtScience</a> <a href="https://sfba.social/tags/Maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#Maths</a> <a href="https://sfba.social/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#Math</a> <a href="https://sfba.social/tags/Infinities" class="mention hashtag" rel="nofollow noopener" target="_blank">#Infinities</a> <a href="https://sfba.social/tags/AC" class="mention hashtag" rel="nofollow noopener" target="_blank">#AC</a> <a href="https://sfba.social/tags/AoC" class="mention hashtag" rel="nofollow noopener" target="_blank">#AoC</a> <a href="https://sfba.social/tags/AxiomOfChoice" class="mention hashtag" rel="nofollow noopener" target="_blank">#AxiomOfChoice</a> <a href="https://www.youtube.com/watch?v=_cr46G2K5Fo" rel="nofollow noopener" translate="no" target="_blank">https://www.youtube.com/watch?v=_cr46G2K5Fo</a>

Insecurity Princess 🌈💖🔥Good news, everyone! Zermelo-Fraenkel File System (ZFS) now supports hot swapping infinitely many hard drives from any arbitrary collection of hard drives! <a href="https://infosec.exchange/tags/ZFS" class="mention hashtag" rel="nofollow noopener" target="_blank">#ZFS</a> <a href="https://infosec.exchange/tags/AxiomOfChoice" class="mention hashtag" rel="nofollow noopener" target="_blank">#AxiomOfChoice</a> <a href="https://www.cyberciti.biz/linux-news/zfs-raidz-expansion-finally-here-in-version-2-3-0/" rel="nofollow noopener" translate="no" target="_blank">https://www.cyberciti.biz/linux-news/zfs-raidz-expansion-finally-here-in-version-2-3-0/</a> <a href="https://mastodon.social/@nixCraft" class="u-url mention" rel="nofollow noopener" target="_blank">@nixCraft</a>

HoldMyTypeI don't post on <a href="https://mathstodon.xyz/tags/mathoverflow" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathoverflow</a> , but when i do <a href="https://mathoverflow.net/questions/434279/two-credible-references-seem-to-differ-on-the-equivalence-of-induction-and-well" rel="nofollow noopener" target="_blank">https://mathoverflow.net/questions/434279/two-credible-references-seem-to-differ-on-the-equivalence-of-induction-and-well</a> <a href="https://mathstodon.xyz/tags/linearorder" class="mention hashtag" rel="nofollow noopener" target="_blank">#linearorder</a> <a href="https://mathstodon.xyz/tags/newfoundations" class="mention hashtag" rel="nofollow noopener" target="_blank">#newfoundations</a> <a href="https://mathstodon.xyz/tags/axiomofchoice" class="mention hashtag" rel="nofollow noopener" target="_blank">#axiomofchoice</a> <a href="https://mathstodon.xyz/tags/zornslemma" class="mention hashtag" rel="nofollow noopener" target="_blank">#zornslemma</a> <a href="https://mathstodon.xyz/tags/induction" class="mention hashtag" rel="nofollow noopener" target="_blank">#induction</a>

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