(Axiomatic Set Theory, 9) Axiom of Foundation

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We discuss the axiom of foundation.
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If S is a non-empty set, then S contains an element which is disjoint with S. If we posit that only sets may be elements of sets and/or proper classes, we can write ⊢ ((S ∈ 𝑉 ∧ S ≠ ∅) → ∃𝑥 ∈ S (𝑥 ∩ S) = ∅)

RichardPenner
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