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I changed back to the previous version for the following reasons:
AxelBoldt, Thursday, April 18, 2002
I gave the notation 1M and a reference. Who uses the notation idM ? Multiplication by one is not restricted to positive integers but apply to any group. Bo Jacoby 10:43, 12 October 2005 (UTC)
Your statement is just a very special case of the more general statement regarding vector spaces. That's why I removed it. There is no reason for restricting the integers to be positive. Nor is there a reason for restricting the numbers to be integers. Nor is there a reason for restricting the vectors to be numbers. In every case where multiplication by 1 makes sense, it represents an identity function. See my point ? I don't mind your removing my reference. (Someone might request a reference if I didn't provide it). Bo Jacoby 09:12, 14 October 2005 (UTC)
OK, now I see what you mean! I might not be the only reader who get more confused than enlightened by this reference to advanced number theory in an extremely elementary context. How many of your readers do you expect to look for this information under the heading Identity function ? I think none. Bo Jacoby 10:04, 17 October 2005 (UTC)
I disagree with a merge. Yes, these are related functions, actually both of them work by f(x)=x. However, the two articles look at the matter from a very different perspective. Typically one uses inclusion maps when one thinks of embedding a space into another, bigger space. The identity function on the other hand shows up when one deals with automorphisms of a given space, and related business. That is to say, it is true that both the identity function and the inclusion map have the formula f(x)=x, but that's all they have in common. Oleg Alexandrov ( talk) 11:08, 20 October 2005 (UTC)
That is interesting. I leaned that function f equals function g if def(f)=def(g) and f(x)=g(x) for all x in def(f). f is injective if f(x)=f(y) implies x=y. f is surjective on B if for every y in B there exists an x in def(f) such that y=f(x). For example. f(x)=x2 (x in R), is not surjective on R, but is surjective on R+. So, strictly speaking, surjectivity is not a property of the function, but of the function f together with the codomain B. Is there any point in distinguishing functions having the same domain and the same values for the same arguments ? Bo Jacoby 17:37, 23 October 2005 (UTC)
Could someone, please, explain, in plain English why the Identity function is useful?
What kind of applications does it have? — Preceding unsigned comment added by 86.156.199.76 ( talk) 01:58, 13 October 2012 (UTC)
@ Dedhert.Jr, the fact that the identity function is denoted idX does not require a reference imho. It it definitely overkill.
But even if you'd disagree, then still the reference you provided does not show that the identity function is "often denoted" as such. It is just a reference that uses the same symbolism. It doesn't mention common use of the symbol whatsoever. Roffaduft ( talk) 14:11, 3 April 2024 (UTC)
This is the
talk page for discussing improvements to the
Identity function article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
I changed back to the previous version for the following reasons:
AxelBoldt, Thursday, April 18, 2002
I gave the notation 1M and a reference. Who uses the notation idM ? Multiplication by one is not restricted to positive integers but apply to any group. Bo Jacoby 10:43, 12 October 2005 (UTC)
Your statement is just a very special case of the more general statement regarding vector spaces. That's why I removed it. There is no reason for restricting the integers to be positive. Nor is there a reason for restricting the numbers to be integers. Nor is there a reason for restricting the vectors to be numbers. In every case where multiplication by 1 makes sense, it represents an identity function. See my point ? I don't mind your removing my reference. (Someone might request a reference if I didn't provide it). Bo Jacoby 09:12, 14 October 2005 (UTC)
OK, now I see what you mean! I might not be the only reader who get more confused than enlightened by this reference to advanced number theory in an extremely elementary context. How many of your readers do you expect to look for this information under the heading Identity function ? I think none. Bo Jacoby 10:04, 17 October 2005 (UTC)
I disagree with a merge. Yes, these are related functions, actually both of them work by f(x)=x. However, the two articles look at the matter from a very different perspective. Typically one uses inclusion maps when one thinks of embedding a space into another, bigger space. The identity function on the other hand shows up when one deals with automorphisms of a given space, and related business. That is to say, it is true that both the identity function and the inclusion map have the formula f(x)=x, but that's all they have in common. Oleg Alexandrov ( talk) 11:08, 20 October 2005 (UTC)
That is interesting. I leaned that function f equals function g if def(f)=def(g) and f(x)=g(x) for all x in def(f). f is injective if f(x)=f(y) implies x=y. f is surjective on B if for every y in B there exists an x in def(f) such that y=f(x). For example. f(x)=x2 (x in R), is not surjective on R, but is surjective on R+. So, strictly speaking, surjectivity is not a property of the function, but of the function f together with the codomain B. Is there any point in distinguishing functions having the same domain and the same values for the same arguments ? Bo Jacoby 17:37, 23 October 2005 (UTC)
Could someone, please, explain, in plain English why the Identity function is useful?
What kind of applications does it have? — Preceding unsigned comment added by 86.156.199.76 ( talk) 01:58, 13 October 2012 (UTC)
@ Dedhert.Jr, the fact that the identity function is denoted idX does not require a reference imho. It it definitely overkill.
But even if you'd disagree, then still the reference you provided does not show that the identity function is "often denoted" as such. It is just a reference that uses the same symbolism. It doesn't mention common use of the symbol whatsoever. Roffaduft ( talk) 14:11, 3 April 2024 (UTC)