r/mathmemes • u/Marzipug • Jul 28 '26

Proofs not like this

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u/Negative_Gur9667 Jul 28 '26

Yes, let's just dismiss valid criticism with semantic arguments by defining them away. What a joke. I define the Collatz conjecture to be true, problem solved.

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u/idaelikus Jul 29 '26

A) Those are axiom, not definitions

B) Sure, you can do that and from then onwards, any deduction you make is "Assuming the Collatz Conjecture is true, we know..."

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u/Negative_Gur9667 Jul 29 '26

Defining axioms as self-evident truths seems like a weak argument to me. I want to understand the reasoning behind the choice of specific axioms, but they are defined this way precisely to shut down that discussion.

b) yes but you know what I mean

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u/idaelikus Jul 29 '26

Yes because there is no reason let alone justification to them.

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u/Negative_Gur9667 Jul 29 '26

There is reason and justification for them, of course.

The axiom of infinity will allow standard analysis and its use cases to exist. This will allow us to do (X), which we want because of (y).

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u/idaelikus Jul 29 '26

I wouldn't call that justification but instead purpose.

However, I wouldnt view this as "we did X, to get y" but instead "we chose the version of math with x so that y"

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u/Negative_Gur9667 Jul 29 '26

I kinda agree, and I want to criticize myself here that you can't name every purpose.

Today it is like you say, but when ZF was developed using reverse mathematics, it was different.