Talk:Zermelo-Fraenkel Axioms

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Zermelo-Fraenkel Axioms was the AoPSWiki Article of the Day for December 20th, 2007

I believe the axiom of infinity is incorrect; shouldn't it be that for all $a \in A$, $a \cup \{a\} \in A$ as well?

Actually, the two forms are equivalent. There are in fact infinitely many possible different axioms of infinity, all of which are equivalent. The weakest and least specific of these infinitely many forms of the axiom is this:

  • There exists a set $A$ and a non-surjective injection $s: A \to A$.

I intend to write an article about this in a few days. Also, please sign your name when you write on talk pages using four tildes (~~~~). —Boy Soprano II 15:12, 16 December 2007 (EST)