[seqfan] Re: Please name this function.

[Charles Greathouse]

If f(x+y) = f(x) + f(y) for all x and y, then f(x) = kx for some fixed
k. If f(xy) = f(x)f(y) for all x and y then f(1) = f(1)^2 and so f(1)
is 0 or 1. In the former case you get f(x) = 0 and in the latter case
you get f(x) = x. Are you looking for a name for this disjunction?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Sat, Sep 8, 2012 at 11:57 PM, Ed Jeffery <lejeffery7 at gmail.com> wrote:
> Thanks Neil, but the identity map would just be f(x+y) = x+y and f(x*y) =
> x*y, which is not what I notated.
>
>> The identity map!
>
>>>* What is the name of a function that is both additive and multiplicative but*>>* not arithmetic (in the sense that x and y are usually not integers), such*>*> that*>>**>*> f(x+y) = f(x)+f(y)*>>**>*> and*>>**>*> f(x*y) = f(x)*f(y)?*
>
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