What is...the axiom of choice?
Goal. I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much. This time. What is...the axiom of choice? Or: It works even if you don’t believe in it. Disclaimer. Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references. Slides. http://www.dtubbenhauer.com/youtube.html Axiom of choice. https://plato.stanford.edu/entries/ax... https://en.wikipedia.org/wiki/Axiom_o... Books. https://link.springer.com/chapter/10.... https://www.gwern.net/docs/math/1973-... https://www.springer.com/gp/book/9783... Russell’s paradox. https://plato.stanford.edu/entries/ru... https://en.wikipedia.org/wiki/Russell... Liar paradox. https://en.wikipedia.org/wiki/Liar_pa... Self-reference. https://mathwithbaddrawings.com/2016/... https://en.wikipedia.org/wiki/Self-re... https://en.wikipedia.org/wiki/List_of... Zermelo-Fraenkel and other set theories. https://en.wikipedia.org/wiki/Zermelo... https://en.wikipedia.org/wiki/Von_Neu... https://en.wikipedia.org/wiki/Von_Neu... https://en.wikipedia.org/wiki/Tarski%... https://en.wikipedia.org/wiki/Constru... https://en.wikipedia.org/wiki/Interna... Axiom of induction. https://en.wikipedia.org/wiki/Epsilon... https://en.wikipedia.org/wiki/Axiom_o... Foundations of mathematics. https://en.wikipedia.org/wiki/Foundat... https://mathoverflow.net/questions/87... https://mathoverflow.net/questions/76... http://www.andrew.cmu.edu/user/awodey... Reverse mathematics. https://en.wikipedia.org/wiki/Reverse... https://press.princeton.edu/books/har... https://www.ams.org/journals/notices/... Mathematica. https://mathworld.wolfram.com/Zermelo... Pictures used. https://mathwithbaddrawings.com/2016/... https://en.wikipedia.org/wiki/Brick#/... https://www.researchgate.net/figure/T... https://en.wikipedia.org/wiki/Horsesh... The axiom of choice is very popular. • How the Axiom of Choice Gives Sizeless Set... • Choice Functions & The Axiom of Choice | N... • What's so wrong with the Axiom of Choice ?
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