Talk:Identity (mathematics)

message: What about this symbol?  : ≡--83.219.124.34 (talk) 23:28, 16 December 2007 (UTC)
thread_title:  Symbol ≡ 

message: 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)
replies: text: 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)
thread_title:  My correction was reverted 

message: 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)
replies: text: 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)
thread_title:  Relations vs Functions 

message: 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)
replies: text: 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)
replies: text: 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)
thread_title:  Definitions