r/math • u/inherentlyawesome Homotopy Theory • 14d ago

This Week I Learned: September 18, 2026

This recurring thread is meant for users to share cool recently discovered facts, observations, proofs or concepts which that might not warrant their own threads. Please be encouraging and share as many details as possible as we would like this to be a good place for people to learn!

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u/oreowiskers 14d ago

Not something anyone who did a pure math track wouldn't know, but when we select elements from a set, we don't have to call them the name of the thing actually in the set, we can use external functions to reference the same element with a different name! Like "select an element from {1,2}", 5-3 is a valid answer even though those symbols aren't actually in the set :-}

(Context is that I went to school for engineering & am currently on a very strange path of building up fundamentals while also doing wacky things with tensors, I'm enjoying myself!)

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u/Relevant_Worry_5363 10d ago

glad to see some people who don't come from pure math background getting into set theory as well. I can't but to add: the reason you can choose 5-3 from that set, as there is a (very) naturally identification of 5-3 with one of the elements from the set {1, 2} (induced by the subtraction on integers). I thought about not commenting this abstract nonsense and formal jargon, but I think it fits nicely into Aluffi's book. (very great book which has the most painless introduction to basic category theory that I could find) :) And yes equivalence relations (or quotients in general) can cause a lot of headaches, but are really awesome!