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)

18Dec2019 --Gbgustafson (talk) 11:39, 18 December 2019 (EST): Browsing for good examples, and this was one. The Historical notes are interesting, appearing in two places (likely non-standard).


 * don't understand, there's only one Historical Notes section. --prime mover (talk) 11:43, 18 December 2019 (EST)
 * OK--Gbgustafson (talk) 12:33, 18 December 2019 (EST). Then let me explain further. There is a section Existence of Empty Set which consists of Historical Notes. I liked the info there. Then I found the Historical Notes later and wondered why they are in two places, when in 2019 the Historical Notes on new pages are collected (hence the reference non-standard). Please take previous remarks as a FaceBook like with no negatives. Curious me, I am trying to understand the logic for creating ProofWiki pages in 2020, and I really don't need to know about 2010 ProofWiki standards or the weather last month in Newfoundland. Collected so far is a list of really excellent ProofWiki pages and what they illustrate for novices like me. I'll send the not very long list with comments at a later date. We are baking Christmas cookies and sending holiday greetings after a short period of very cold weather, which has now turned into fall temperatures and sunny days with only one snow day in the holiday season. The tea kettle sings. Falcons search for dinner. Us too.


 * Existence of Empty Set is not' historical notes.


 * "I am trying to understand the logic for creating ProofWiki pages in 2020," ... no, there is no logic to it, it's a complete and utter waste of everybody's time and effort. --prime mover (talk) 12:48, 18 December 2019 (EST)