Which axiom of set theory forbids a mathematical object to be an element of a set and not be an element of the very same set?
2026-04-01 15:07:15.1775056035
Axiom of set theory wanted
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As Nate Eldredge has noted, the axiom will not be given in the set theory, but rather in the underlying (probably first-order) logic. In general, the assertion is given as $\neg (\psi \wedge \neg \psi)$, where $\psi$ is some predicate, basically saying that nothing can be true and false at the same time. It is referred to as the law of non-contradiction and is part of classical logics.