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**akolman** Hi, how would you solve the following problem

**Prove:** If $\displaystyle f(x)$ is defined on $\displaystyle \Re $ and continuous at $\displaystyle x=0$, and if $\displaystyle f(x)=f(x_{1})+f(x_{2})$ $\displaystyle \forall x_{1},x_{2} \in \Re $, then $\displaystyle f(x)$ is continuous at all $\displaystyle x \in \Re $

Thanks in advance

By the way, is there a theorem that clearly states that any real number can be expressed as the sum of two other real numbers? I'm guessing this is a big part of the proof.