Talk:Symmetric difference

On repeating links in the "see also" section

JA: Not that big of a deal, but it can be very useful to the reader, both on first and subsequent readings of an article, to have a syllabus of related topics collected in one place. For instance, I think of the times I myself spend looking for a topic I know I saw in some topical connection but can't rememeber where and it's too much of a hassle searching through multiple texts. No trees were harmed in the making of these compendia. Jon Awbrey 04:15, 12 March 2006 (UTC)[reply]

[1] I don't feel strongly about it, you may put some back if you wish. :) Oleg Alexandrov (talk) 04:45, 12 March 2006 (UTC)[reply]

Balking at "equivalence" with XOR

I've just changed the first paragraph, which did call symmetric difference the "set-theoretic equivalent" of exclusive disjunction. For me, that's too much abuse of terminology (viz. equivalent), especially in an article on a mathematical topic. So I've merely replaced equivalent with kin. My replacement is no less vague, but at least its imprecision is more above board.—PaulTanenbaum (talk) 13:03, 28 January 2008 (UTC)[reply]

References?

Does anyone have references to where to find this in the (printed) literature ? Who first introduced the symmetric difference (pseudo)metric? —Preceding unsigned comment added by 193.190.253.149 (talk) 12:08, 21 May 2008 (UTC)[reply]

Symmetric difference symbol, $A\,\Delta \,B$ or $A\ominus B$ ?

Does anyone know which of the two symbols is more commonly used? – Fuzzy – 13:09, 17 August 2011 (UTC)[reply]

There is no one standard notation. I have never seen

\ominus

used in math. I believe it's an error in Wolfram MathWorld (which is not a reliable source). (It makes no sense for a symmetric operation.) Common notations are

\Delta ,\ \triangle ,\ \oplus

. Others are sometimes used. Zaslav (talk) 06:10, 30 September 2023 (UTC)[reply]

I changed it from vartriangle to Delta in accordance with the following links.^[1]^[2]^[3]^[4]^[5]

relation to multisets

Can someone source and make more precise the statements in relation to multisets. They were state with "is" which was obviously an abuse of language, so I've changed it to "equivalent". But in what precise (say categorical) sense are these equivalent? 86.127.138.67 (talk) 16:56, 9 April 2015 (UTC)[reply]

Delta versus triangle

This edit by DanBLOO replaced the consistent use of the LaTeX command \triangle ( $A\triangle B$ ) with consistent use of the LaTeX command \Delta ( $A\Delta B$ ). I am not particularly convinced this is correct, but not skeptical enough to simply revert. Unfortunately the article has no good sources that discuss the notation or its history (in contrast with, say, Empty set). Thoughts? --JBL (talk) 17:18, 2 July 2023 (UTC)[reply]

i'm no expert on this, but i made the change based on what the delta letter article says, as well as Δ on Wiktionary, and sources like this. danBLOO (talk) 00:20, 4 July 2023 (UTC)[reply]

The original notation seems to be

\Delta

but has been largely replaced by other notations, such as

\triangle

. I don't know sources for this aside from my memory of notation 60 years ago. Zaslav (talk) 06:06, 30 September 2023 (UTC)[reply]

Unreliable MathWorld

I have found MathWorld to have errors too often. I can't say it is a reliable source. In particular it's not accurate for notations for symmetric difference; e.g., it says^[6] "All but [ $\ominus$ ] should probably be deprecated", which is nonsense; that notation is uncommon while others are common. I am removing it as a source. A reliable source would be a good textbook, for example. Zaslav (talk) 06:16, 30 September 2023 (UTC) Zaslav (talk) 06:16, 30 September 2023 (UTC)[reply]

I often reference Wikipedia seeking the "default" notation for an operation. This time, it disagreed with both MathWorld and my textbook, "A Book of Abstract Algebra, Second Edition, Charles C. Pinter, Professor of Mathematics, Bucknell University, Dover Publications, Inc., Mineola, New York", which uses simply +. I believe this article should probably mainly rely on whatever symbol is most commonly used by the sources it cites if anyone wants to check which notation seems most frequent in the cited sources. 75.164.251.60 (talk) 03:49, 10 May 2024 (UTC)[reply]

References

^ "Exclusive disjunction - OeisWiki". oeis.org. Retrieved 10 May 2024.
^ Campbell, John (23 March 2017). "Une classe d'ensembles qui sont fermés sous l'opération de différence symétrique lié aux involutions commutant". Discrete Mathematics & Theoretical Computer Science. doi:10.23638/DMTCS-19-1-8. Retrieved 10 May 2024.
^ Auckly, Dave. "The Symmetric Difference is Associative" (PDF). Dave Auckly's home page. Retrieved 10 May 2024.
^ Lu, Lincoln; Smith, Dustin. "Math 776 Graph Theory Lecture Notes 6: Matchings" (PDF). Math 777 Graph Theory (II), Spring 2006. Retrieved 10 May 2024.
^ Daileda, Ryan. "Associativity of the Symmetric Difference" (PDF). Spring 2012 - Partial Differential Equations. Retrieved 10 May 2024.
^ Weisstein, Eric W. "Symmetric Difference". mathworld.wolfram.com. Retrieved 2023-09-26.

ThoughtCo

It is NOT the best source and should probably not be the first source for this article. 75.164.251.60 (talk) 03:56, 10 May 2024 (UTC)[reply]

[1] "Exclusive disjunction - OeisWiki". oeis.org. Retrieved 10 May 2024.

[2] Campbell, John (23 March 2017). "Une classe d'ensembles qui sont fermés sous l'opération de différence symétrique lié aux involutions commutant". Discrete Mathematics & Theoretical Computer Science. doi:10.23638/DMTCS-19-1-8. Retrieved 10 May 2024.

[3] Auckly, Dave. "The Symmetric Difference is Associative" (PDF). Dave Auckly's home page. Retrieved 10 May 2024.

[4] Lu, Lincoln; Smith, Dustin. "Math 776 Graph Theory Lecture Notes 6: Matchings" (PDF). Math 777 Graph Theory (II), Spring 2006. Retrieved 10 May 2024.

[5] Daileda, Ryan. "Associativity of the Symmetric Difference" (PDF). Spring 2012 - Partial Differential Equations. Retrieved 10 May 2024.

[6] Weisstein, Eric W. "Symmetric Difference". mathworld.wolfram.com. Retrieved 2023-09-26.

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