- #1

- 7,006

- 10,459

Hi, we know that using choice * that we can find a function ## f: \mathbb R \rightarrow \mathbb R ## so that ## f(x+y)=f(x)+f(y) ## , but f is not linear. Is the "other way" possible, i.e., can we have :

## g: \mathbb R \rightarrow \mathbb R ## so that, for all Real constants c, all Real values x , we have

## g(cx)=cg(x) ## , but ## g(x+y ) \neq g(x)+g(y) ## for all x,y ?

* I guess I am pro-choice ;).

## g: \mathbb R \rightarrow \mathbb R ## so that, for all Real constants c, all Real values x , we have

## g(cx)=cg(x) ## , but ## g(x+y ) \neq g(x)+g(y) ## for all x,y ?

* I guess I am pro-choice ;).

Last edited: