Given a linear function $T: \Bbb R \rightarrow \Bbb R$ and $T(x+y) = T(x) + T(y)$, do we have that $T(x) = s(x)$ for some $s \in \Bbb R$
I'm doing an exam review for my analysis class but the professor said this has to do with rings and fields and I'm not sure how to rigorously show this using analysis.
My idea for the proof is to let $x = 0,1$ but I feel like those are the trivial cases. Any help is appreciated!