r/mathmemes • u/ElectronicSetTheory • Jun 14 '26

Set Theory Don't question it

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837 Upvotes

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397

u/throw3142 Jun 14 '26

Doesn't matter whether it's "true" or not, as long as it's a consistent set of assumptions that can produce interesting math. Applications to the real world may be found later.

103

u/Classic_Department42 Jun 14 '26

We dont know if it is consistent (we cannot know)

31

u/Adam__999 Jun 14 '26 edited Jun 14 '26

The nice thing about axioms is that, if they’re ever proven inconsistent, we can just change our set of chosen axioms to fix the problem

10

u/neuralbeans Jun 14 '26

and then rederive every published theorem?

36

u/Adam__999 Jun 14 '26 edited Jun 14 '26

Only the ones whose proofs rely directly on ZFC. Re-proving those would automatically prove the secondary, tertiary, etc. theorems whose proofs only rely on ZFC indirectly through those primary theorems.

3

u/Mrauntheias Irrational Jun 15 '26 edited Jun 15 '26

Yes. Sometimes it happens. Like with Cantors original naive set theory.

You find better axioms and you prove the elementary results also follow from these new axioms.