Talk:Universe (mathematics)

Weirdness
A former version of this article was rather weird, and nobody understood it: so it was nominated for deletion, until Toby Bartels saved the day. Three cheers for Toby! :)


 * Gosh, thanks. ^_^ -- Toby Bartels

From the deletion nomination:
 * A mathematician should look at this - it seems like oddball city to me. --mav 04:56, 15 Aug 2003 (UTC)
 * I am a mathematician, and I agree [with deletion]. I believe it was written in good faith and that it took real effort but that it doesn't belong in the wikipedia. Michael Larsen 10:36, 15 Aug 2003 (UTC)
 * makes absolutely no sense to me. seems like disinformation --Alex.tan 06:29, 15 Aug 2003 (UTC)
 * Typical quackpot ramble. Andre Engels 10:47, 15 Aug 2003 (UTC)
 * Nonsense - delete it. This should contain an entry on the set-theoretical term "Universe". -- Schnee 23:33, 16 Aug 2003 (UTC) (mathematician)
 * I think that I've got a good start on a real article there now. BTW, some of that old stuff actually some sense in it too, but well buried under the overenthusiasm, lack of precision, and POV. Look up Douglas Sweetser on the Internet if you want to see more of it; or look up David Hestenes in the library if you want something similar but sensible. -- Toby Bartels 14:33, 21 Aug 2003 (UTC)

Notation
power set notation: is it clearer to write PX or P(X) ? Martin

I prefer the simplicity of "PX". Actually, I really like
 * $$ \mathcal{P}X \! $$,

but that would be unnecessary dependence on images IMO. I would hope that "PX" is confusing only to those poor benighted souls that believe that function application is always denoted by parentheses, but a little reflection on one's days in trigonometry can usually cure that. To be sure, there's nothing at all wrong with "P(X)", and I would hardly change an article that already used such notation! -- Toby Bartels 07:20, 24 Aug 2003 (UTC)

For "poor benighted souls", read "programmers" :) I'll leave it be. Martin

In case anybody in the future decides to change it, note that the notations PX and SX are serving largely analogous roles. So their markups should be similar. (Similarly, the subscripts in SiX, Li, and Vi are analogous.) -- Toby Bartels 19:59, 28 Jan 2004 (UTC)

I have some questions about set universes. I can construct a set universe starting from any give set, right? The last sentences of the set theory section tell me that I will always get the standard set universe (starting with {}). Is that right? As far as I know, the power class of a class X is defined to be the class of all subsets of X. If this is so, what is the power class of the set universe? Is it the universe itself? --SirJective (217.80.240.75 20:36, 4 May 2004 (UTC))

---

Comment more than question. For the less mathmatically inclined, this post is largely useless. Being one of those less inclined individuals, I'm dumfounded by the language, context, and general layout of most of the information. Now, do not take this as an attack on the post, but a criticism of its accessibility. Just a thought, and I know its possible, my text books do a decent job of it. -extra-ultra-super-cataclysmically benighted soul

Another notation question: why write 'The empty set is the von Neumann ordinal [0]' instead of just 'The empty set is the von Neumann ordinal 0'? 86.132.223.25 (talk) 11:31, 4 February 2014 (UTC)

In Computer Science
I think that the "In Computer Science" section should be moved to the logic gate article or to another new entry all by itself, since the entire rest of this article is concerned only with the mathematical concepts of Universe. -Loadmaster 23:27, 15 June 2006 (UTC)


 * Moved to a top sentence; there wasn't any content there. I guess someone could start an article on expressive adequacy. EdC 03:58, 27 June 2006 (UTC)

Paradox
Isn't there an old paradox about the Universe containing itself? I assume that's been resolved, but it would be nice to see that resolution here. --Joel 05:36, 22 October 2006 (UTC)


 * Yes, there is a substantial body of work on avoiding the paradoxes in set theories with a universal set, i.e., with a set which contains itself. See Forster's Oxford Logic Guide Set Theory with a Universal Set.  I'll start the requested clean-up by breaking the redirect from “Universal set” to this page, which is almost entirely about universal classes (which are not members of themselves), not a universal set.


 * FlashSheridan 16:49, 31 October 2006 (UTC)\\

Universe vs Universal Set
It would useful to make a distinction between a "universe" in set theory and a "universal set" in set theory - especially since the current Wikipedia article on "Universal set" says:

"In set theory as usually formulated, the conception of a universal set leads to Russell's paradox and is consequently not allowed."

Tashiro~enwiki (talk) 00:13, 22 September 2019 (UTC)

I support adding this distinction to the page. So far both this page and the page on Universe of Discourse refer to the universes been sets. However in FOL it is not necessary that they be sets at all.

Whole Oats (talk) 05:03, 13 June 2020 (UTC)

domain of discourse: in philosophy or in the formal sciences?
"It is related to the concept of a domain of discourse in philosophy". But Domain of discourse: "In the formal sciences, the domain of discourse, also called the universe of discourse..." — Preceding unsigned comment added by Fractaler (talk • contribs) 12:45, 4 August 2020 (UTC)
 * , "domain of discourse" is not mentioned in the article itself, so I've just removed it per MOS:LEAD and MOS:INTRO in particular. —⁠andrybak (talk) 16:17, 4 August 2020 (UTC)
 * Thanks! —⁠Fractaler (talk) 06:54, 5 August 2020 (UTC)