I am trying to understand a proof, I don't understand one of the steps. could someone shed some light why the following is true.
if $f(x)$ is a non-increasing and continuous function and $a>b$ then $\{x\colon f(x) > f(b) \} \subset \{x\colon f(x) > f(a) \} $
i don't see why this is true. any insights ?