Talk:Identity (mathematics)

Old comment (2005)[edit]

hmmm it seems that these various definitions of identity almost need a disambiguation page. Dmharvey Talk 20:54, 3 Jun 2005 (UTC)

I know what you mean, but I've tidied up Identity (disambiguation), and I think it gets the job done. On the other hand, this article doesn't have enough information to split up, does it? Melchoir 01:51, 27 November 2005 (UTC)[reply]

Not enough information at present to warrant separate pages IMO, perahps at a later date. For now, it gets the job done. --DCS 20 December 05

User:Arvind asia I want to know whether the structure of the algebra identity (a - b)2 = a2 - 2ab + b2

Symbol ≡[edit]

What about this symbol? : ≡
--83.219.124.34 (talk) 23:28, 16 December 2007 (UTC)[reply]

My correction was reverted[edit]

I changed this, it was changed back, so I'll put it here.

(Reverted 1 edit by LieAfterLie (talk): This is not an article about element. (TW)) (undo | thank)

(→‎Comparison: moved italic to appropriate word, from 'identity' to 'element') (undo)

"Also, some care is sometimes needed to avoid ambiguities: 0 is the identity element for the addition of numbers and x + 0 = x is an identity."

The first 'identity' was italicized, I changed it to 'element' because it seems odd to emphasize the descriptor that the two things being compared have in common, as if it were the thing that's different, which is actually 'element'. The counterpart for 'identity' here, is 'identity', so why italicize one as if to suggest it's critically different from the other? 'The first is merely an *identity*, while the second is an identity.' It doesn't make sense. The difference to emphasize is between 'element' and 'an', not 'identity' and 'identity'. What does "This is not an article about element." mean? Of course it's not. Are you saying we should italicize all 36 uses of the word identity in the article? Why the first in that sentence and not the second? What's the distinction? Thus why I made the edit, which was then ambiguously reverted. LieAfterLie (talk) 02:06, 6 April 2014 (UTC)[reply]

It appears that you have missed the point of the sentence you wanted to edit. What was intended was a statement that the word "identity" has several different meanings (see the lead section) and unless one is careful, statements using the word can be misinterpreted. In the phrase "0 is the identity element", identity element is the formal name of what zero is with respect to addition. This does not need to be emphasized in that phrase. However, "identity element" is often shortened to just the identity and the emphasis was placed on the word "identity" in that phrase to bring out this special usage. This usage of the word was then compared to "x + 0 = x is an identity", and here identity is being used as a type of equation valid for all values of the variable. So, yes the difference in this sentence was between 'identity' and 'identity' and the emphasis was needed where it was placed to make the distinction. Bill Cherowitzo (talk) 04:26, 6 April 2014 (UTC)[reply]

Relations vs Functions[edit]

It is inadequate to characterize mathematical identity as equality of functions since mathematical logic recognizes equality not only of functions, which are N:1 relations, but of relations generally. See Identity_of_indiscernibles#Identity_and_indiscernibility. Jim Bowery (talk) 13:44, 30 September 2015 (UTC)[reply]

This article is about identity in mathematics. As it occurs frequently, the mathematical meaning of the word is not exactly the same as in common language or in other fields. The article to which you refer is about identity in philosophy, and is thus irrelevant here. In Wikipedia, a definition cannot be inadequate: either it is commonly used, and it must appear as it is used in textbooks, or it must be removed from Wikipedia. "Identity", is no more used in advanced mathematics, but is still commonly used in elementary courses. Therefore, the definition given here is adequate, or more precisely relevant. In mathematics, identity is not the same as equality. Equality is defined for every mathematical object, including functions and relations. On the other hand, identity is not a relation between objects, but between their representations in term of expressions. On the other hand the article Identity_of_indiscernibles seems to be more related to what mathematicians call "equality up to a canonical isomorphism" than to this article. D.Lazard (talk) 15:25, 30 September 2015 (UTC)[reply]

Requested move 16 November 2016[edit]

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. No further edits should be made to this section.

The result of the move request was: not moved. Andrewa (talk) 20:21, 24 November 2016 (UTC)[reply]

Identity (mathematics) → Mathematical identity – Renaming the page would remove parentheses, and parentheses should be avoided when possible. In addition, there is already a page called "List of mathematical identities", indicating that the term "mathematical identity" is in common use. The target is a redirect to this article with no other edits, so I could move it myself, but I felt that a discussion first would be good. HotdogPi 10:26, 16 November 2016 (UTC)[reply]

Oppose: The terms are not synonymous: a "mathematical identity" is a theorem, while "identity" is, in mathematics, a kind of equality relation, which should not be confused with equality. Presently, this article is a stub, as the topic "identity" is described only in the introduction, but many things deserve to be added, which cannot belong to the target of the proposed merge. For example, an history section is lacking, which should explain why, at some periods, the sign $\equiv$ were widely used, and why it is presently old fashioned. D.Lazard (talk) 11:22, 16 November 2016 (UTC)[reply]
Comment – what about moving the page to Identity in mathematics? This is WP:NATURAL but accurately reflects the scope of the topic, opposed to a non-synonymous term like mathematical identity. CookieMonster755 𝚨-𝛀 05:11, 18 November 2016 (UTC)[reply]
Oppose. "Identity" in this case is a technical term in the field of mathematics. "Mathematical identity" makes that unclear, and "Identity in mathematics" makes it seem akin to 1999 in music, which is an unnatural disambigation to me. I believe the existing name is the best disambiguation. —Gordon P. Hemsley→✉ 07:56, 24 November 2016 (UTC)[reply]

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Definitions[edit]

These definitions tells me nothing. It's formal gobbledygook pretentious wording nonsense. How can an average person understand this. --Ejenriquez (talk) 06:01, 25 October 2021 (UTC)[reply]

Which definitions do you mean? I didn't find any formal definition, but only example identities. If I were to define "identity" formally, I'd say it is the universal closure of an equation, but I don't have a source for this at hand. - Jochen Burghardt (talk) 09:51, 25 October 2021 (UTC)[reply]

Apparently, this editor is unable to understand the first phrase of this article ("In mathematics"), and has never learnt that, to understand a technical text, one has first to learn the basic terms of the corresponding technical language. D.Lazard (talk) 10:22, 25 October 2021 (UTC)[reply]