[seqfan] Re: Please name this function.

[Neil Sloane]

Ed, let me expand on my answer. You said x,y need not be integers,
so I assumed your f is a map from the reals to the reals.
Now watch:
f(x+0)=f(x)+f(0) -> f(0)=0
f(x*1)=f(x)f(1) -> f(1)=1
f(x+x)=2f(x)=f(2x)=f(2)f(x)->f(2)=2
Simly f(k)=k for k integer
Simly f(1/k)=1/k
Simly f(j/k)=j/k
f is continuous, so f(x)=x for x real
So f=identity

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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