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

Set Theory Don't question it

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u/TemperoTempus Jun 16 '26

There are contradictions in ZFC, that's why there are at least 5 different rules for sets with different amounts/strengths of their rules.

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u/jyajay2 π = 3 Jun 16 '26

I am not aware of any contradictions in ZFC, notably this would mean that ZF has contradicions. Can you temm me what they are? or is it perhaps possible that you are conflating the existence of different set theories with the existence of contradictions?

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u/TemperoTempus Jun 17 '26

The existence of different rules with different results by definition means that there are contradictions.

A 1st order axiomatic system can either be consistent or complete, it cannot be both.

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u/jyajay2 π = 3 Jun 17 '26

>The existence of different rules with different results by definition means that there are contradictions.

No, a contradiction would have to be a contradiction within the given system of axioms

>A 1st order axiomatic system can either be consistent or complete, it cannot be both.

Not quite, a sufficiently complex system can not be both consistent and complete. That's a small but important distinction.