TITLE: Ring of all continuous functions from reals into reals is not integral domain
QUESTION [9 upvotes]: Let $R$ be the ring of all continuous functions from the real numbers into the real numbers. Prove that $R$ is not an integral domain. 
I need help with this. I do not understand this at all and my book really doesn't give that much information.

REPLY [4 votes]: For example
$$f(x)=\begin{cases}0&,\;\;x\le 0\\{}\\x&,\;\;x\ge 0\end{cases}\;\;\;,\;\;g(x)=\begin{cases}x&,\;\;x\le 0\\{}\\0&,\;\;x\ge 0\end{cases}$$