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 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)
- 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 idM, while Herrlich, Horst and Strecker, George E.; Category Theory, Allen and Bacon, Inc. Boston (1973), uses 1M. — Paul August ☎ 18:39, 13 October 2005 (UTC)
- 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)
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)