Novice mathematician here, please forgive the simple question. I have encountered the following expression in one of my textbooks and can't work out how to interpret its right side:
$$ g(x) = \max\{x-150,0\} $$
Is the $0$ after the comma in the curly brackets a rule that helps define a set?
No, it's an element.
When you write $g(x)=\max\{x-150,0\}$ it means that, for any $x$, $g(x)$ is the maximum of the set $\{x-150,0\}$. For instance, $$x=1\implies \max\{x-150,0\}=\max\{1-150,0\}=0\\ x=153\implies\max\{x-150,0\}=\max\{153-150,0\}=3$$