Talk:Identity function

I changed back to the previous version for the following reasons:

The identity function is in general not multiplicative. Only in the special case of M = positive integers could it be called a multiplicative function. But there are many other sets M out there.
We don't use colors in formulas
Blackboard bold is reserved for sets of numbers, like R or C. Letters that stand for functions, sets or variables are normally written in italic.

AxelBoldt, Thursday, April 18, 2002

I gave the notation 1_M and a reference. Who uses the notation id_M ? Multiplication by one is not restricted to positive integers but apply to any group. Bo Jacoby 10:43, 12 October 2005 (UTC)[reply]

I've rewritten the notation bit a little, and removed the reference to Jean-Marie Souriau. There is no need to mention a specific user of either notation, since both notations are common I think, for example: Adámek, Jiří, Herrlich, Horst, & Strecker, George E.; (1990). Abstract and Concrete Categories uses id_M, while Herrlich, Horst and Strecker, George E.; Category Theory, Allen and Bacon, Inc. Boston (1973), uses 1_M. — Paul August ☎ 18:39, 13 October 2005 (UTC)[reply]

I've also restored the fact that:

The identity function on the positive integers is a multiplicative function (essentially multiplication by 1), considered in number theory.

I believe this statement is correct. I don't understand why it was removed. — Paul August ☎ 18:39, 13 October 2005 (UTC)[reply]

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)[reply]

Yes in any algebraic structure which possesses a mutiplicative identity, multiplication by that identity will be the identity function, but such functions are not generally called multiplicative. The reason for restricting to positive integers is because that is the ony context in which a multiplicative function is defined. The term is not, to my knowledge, used outside of number theory. Paul August ☎ 16:54, 14 October 2005 (UTC)[reply]