4
Can I say:
$$\sup |f(x)-h(x)+g(x)-g(x)| = \sup|f(x)-g(x)|+ \sup|g(x)-h(x)|$$
I can't seem to find any properties of $\sup$ , so i am wondering if there is any properties that we can generalize to sup of some functions restricted on domain $x \in [0,1]$ for example