Definition talk:Empty Set

Removed the definitions based on the universal set because those are covered in their own pages. Also moved the $x \ne x$ definition into the ZF axioms section because (as that's where it is initially defined) that's where it goes. --prime mover 00:27, 13 September 2011 (CDT)

Look at what $\exists$ means
I don't understand. --prime mover (talk) 03:36, 6 November 2016 (EST)


 * If you follow my little link to Definition:Existential Quantifier, you would find that $\exists$ uses the empty set, so you cannot use $\exists$ in the definition of an empty set... --kc_kennylau (talk) 03:38, 6 November 2016 (EST)


 * Okay so that's something else that will need to be deleted and re-done: the axiomatic development of the number systems. Deleted, anyway, whether there's any point in trying to redo it is anybody's guess. --prime mover (talk) 04:32, 6 November 2016 (EST)

The problem is in the purportedly axiomatic definition of $\exists$. It being part of the formal language of predicate logic precludes it from being defined in terms of ZF.

Also, the page only defines $\exists x \in S: P(x)$, and not "$\exists$" in its own right. So this needs to be addressed on Definition:Existential Quantifier. &mdash; Lord_Farin (talk) 05:45, 6 November 2016 (EST)