Axiom of foundation

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[ilmath]\newcommand{\limplies}[0]{\rightarrow} [/ilmath]

Definition

• [ilmath]\forall S\big[S\neq\emptyset\limplies\exists x[x\in S\wedge S\cap x\eq\emptyset]\big][/ilmath]
  • In words:
    • i.e. every non-empty set has an [ilmath]\in[/ilmath]-minimal element