Max of two functions notation I am working on a proof and the hypothesis included the following function: 
$h(x)=$ max $\{f(x),g(x)\}$
I do not understand this notation or what this is saying. Could someone give me a formal definition and explain what "max" this function is referring to?

You may as well write
$$ h(x)=\begin{cases}f(x)&\text{if }f(x)\ge g(x)\\g(x)&\text{otherwise}\end{cases}$$
