Talk:Subset

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The section "⊂ and ⊃ symbols" only mentions the symbols ⊊ and ⊋ as something some authors prefer not to use. The reference there does not mention these symbols. It would be useful to find a positive reference for authors that do prefer to use ⊊ and ⊋ for proper sub/supersets, and use ⊂ and ⊃ where the two sets may be equal. — Preceding unsigned comment added by Kopretinka (talk • contribs) 10:14, 27 November 2017 (UTC)Reply

There's a whole list at Wikipedia talk:WikiProject Mathematics/Conventions#Literature survey. That's part of what I would call an obsolete discussion from more than a decade ago, but should be a good resource to find authors who do various things. --Trovatore (talk) 19:27, 27 November 2017 (UTC)Reply

It would be useful if the article explains or defines what the proper subset and superset *is* before introducing the symbols for them. 86.12.162.37 (talk) 16:32, 12 January 2018 (UTC)Reply

This is done in the section on definitions, which comes before the section on this notation. --Bill Cherowitzo (talk) 20:03, 12 January 2018 (UTC)Reply

No it's not. I agreed with the OP, it is not clear at all from this article what a *proper* sub-/superset is from this article. I had to look this up on another website. JHBonarius (talk) 08:13, 11 March 2018 (UTC)Reply

Please indicate what part of this is not clear.

If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B which is not an element of A), then

• A is also a proper (or strict) subset of B; this is written as ${\displaystyle A\subsetneq B.}$

or equivalently

• B is a proper superset of A; this is written as ${\displaystyle B\supsetneq A.}$

I copied that from the definitions section. What would you suggest to improve the wording? --Bill Cherowitzo (talk) 18:16, 11 March 2018 (UTC)Reply

I've found a book that uses ⊂,⊃ instead of ⊊,⊋, and introduces the secondary notation as not very common. I don't know how to do citations but the book is "Mathematical Proofs: A Transition to Advanced Mathematics 3rd Edition by Chartrand". If someone could add this to the article it'd be greatly appreciated. — Preceding unsigned comment added by 130.101.12.167 (talk • contribs) 22:27, 2 September 2021 (UTC)Reply

OK, it's true that ⊊,⊋ are not really very common, but that's in part because the notion of strict subset is less important than the notion of subset. Lots of sources use ⊂ for the more important notion, the one sometimes notated ${\displaystyle \subseteq }$. This should be discussed somewhere, but without suggesting that ⊂ normally means strict subset, which isn't true. --Trovatore (talk) 01:47, 3 September 2021 (UTC)Reply

Hipo 175.176.92.201 (talk) 11:14, 31 August 2022 (UTC)Reply

In the "Examples of Subsets" section:

* The set A = {1, 2} is a proper subset of B = {1, 2, 3}, thus both expressions <math>A '''\subseteq''' B</math> and <math>A \subsetneq B</math> are true.
* The set D = {1, 2, 3} is a subset (but {{em|not}} a proper subset) of E = {1, 2, 3}, thus <math>D \subseteq E</math> is true, and <math>D \subsetneq E</math> is not true (false).

• I think \subseteq that I bolded should be \subset. Otherwise both proper and improper subsets are denoted by the same symbol.
• Can someone review this, I'm not a mathematician.

Zeyn1 (talk) 11:30, 19 October 2023 (UTC)Reply

There is nothing here that needs to be fixed. In the first example, ${\displaystyle A\subseteq B}$ and ${\displaystyle A\subsetneq B}$ are both true, as stated, because ${\displaystyle A}$ is both a subset of ${\displaystyle B}$ and a proper subset of ${\displaystyle B}$. (There is no such thing as an "improper subset".) --Trovatore (talk) 14:47, 20 October 2023 (UTC)Reply

Oh, I just realized what you might mean. Are you saying ${\displaystyle \subseteq }$ and ${\displaystyle \subsetneq }$ look the same to you visually? Look closer. The ${\displaystyle \subsetneq }$ symbol has a cross through the line on the bottom. Admittedly it can be a little hard to see sometimes. --Trovatore (talk) 14:59, 20 October 2023 (UTC)Reply

As an aside, does anyone know a single LaTeX command to get something like ${\displaystyle {\stackrel {\subset }{\neq }}}$? There's a symbol that looks a bit like that, but better proportioned, that's sometimes used, and it's easier to see the not-equals part than in ${\displaystyle \subsetneq }$. Could potentially be described in the article, or even used in it. But I haven't been able to find such a thing. --Trovatore (talk) 20:04, 20 October 2023 (UTC)Reply

Ah, here it is: ${\displaystyle \subsetneqq }$. Honestly I think that's much clearer to read. --Trovatore (talk) 20:09, 20 October 2023 (UTC)Reply

Why do we prefer ${\displaystyle \subseteq }$ to ⊆ in the wiki? The current paradigm seems to be ${\displaystyle \subseteq }$ but this text does not copy/paste. In several contexts it seems appropriate to use the Unicode symbol instead: ⊆. Are there already guidelines and rationale for this? Wjmelements (talk) 21:07, 9 October 2024 (UTC)Reply

Hmm. The LaTeX version looks considerably better to my eye (in my browser, using my fonts, etc), but some of this may be down to decisions made in an era in which support for medium-to-obscure unicodes was spotty. It could be worth opening a discussion at WT:WPM. --Trovatore (talk) 18:32, 10 October 2024 (UTC)Reply