Talk:Subset

Symbols ⊊ and ⊋

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)

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)

Proper subset/superset

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)

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)

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)

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 $A\subsetneq B.$

or equivalently

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

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

Requested move 15 September 2020

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: No consensus. User:Ceyockey (talk to me) 01:40, 24 September 2020 (UTC)

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Subset → Subset and superset – Another option would be Subsets and supersets (plural).

This article covers both subsets and supersets. These two concepts are inseparable, and mutually dependent: there cannot be subsets if there aren't supersets. It is therefore illogical to have one term in the title, but not its counterpart.

This page was actually called Subset and superset for a short time back in 2014. On 27 November 2014, the page was moved. The next month, it was moved back, but the rationale given in the log doesn't make much sense to me. Cheers, Manifestation (talk) 19:56, 15 September 2020 (UTC)

• Support per nominator. Every subset has a superset and vice versa. The nominator's original suggestion is fine, no need to move to Subsets and supersets. JIP | Talk 01:03, 16 September 2020 (UTC)
• Comment: pending the decision of the closing admin, I've written a new paragraph for the lead. Feel free to alter/revert if desired. Cheers, Manifestation (talk) 10:56, 20 September 2020 (UTC)
• Oppose. I agree with Trovatore's rationale of 2014. Yes, the terms are, in a sense, equivalent but common usage is to describe things in terms of subsets. Most texts that I have seen hardly ever mention supersets. If we were to follow the reasoning given to its logical conclusion, we would have to change the name of our article Set to Set and complimentary set, which I don't think would get much support. --Bill Cherowitzo (talk) 20:40, 20 September 2020 (UTC)
• Oppose I don't really much care about the title. Much more important is to have a substantive first sentence, and having to explain both in that sentence will complicate it unduly.

The first sentence is currently "Subset and superset are terms used in mathematics." which violates WP:REFERS (it is talking about the names rather than the concepts) and says nothing substantive. Previously, it was phrased in terms of containment, which is not great either; it's yet another concept that the reader may or may not know. Some possibilities that depend only on the idea that a set has elements:

A subset B of set A contains only elements found in set A.

A set B is a subset of set A if all of the elements of B are also elements of A.

I'm sure we can do better.... But the point is that trying to define both in the lead sentence will make it harder to write a clear, simple definition. --Macrakis (talk) 22:18, 20 September 2020 (UTC)

• Comment I've seen a lot of these "foo and foo-dual" titles cropping up. I've never liked them. I do sort of see the point, but I still don't really like them, because their aboutness is muddled. We should maybe have a broader conversation about them, maybe in WT:WPM. --Trovatore (talk) 03:41, 21 September 2020 (UTC)

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The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Better sourcing for subset notation

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)

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 $\subseteq$. 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)

Hi

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

About $\subseteq and \subset$

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)

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

Oh, I just realized what you might mean. Are you saying $\subseteq$ and $\subsetneq$ look the same to you visually? Look closer. The $\subsetneq$ 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)

As an aside, does anyone know a single LaTeX command to get something like ${\stackrel {\subset }{\neq }}$? 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 $\subsetneq$. 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)

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