Supposing $f: [0,\infty) \to [0,\infty)$. The goal is to make an increasing function from $f$ using the following rule:-
If $t_1 \leq t_2$ and $f(t_1) > f(t_2)$ then change the value of $f(t_1)$ to $f(t_2)$.
After this change, we have $f(t_1) = f(t_2)$.
Let $g$ be the function resulting from applying the above rule for all $t_1,t_2$ recursively (recursively because if $f(t_2)$ changes then the value of $f(t_1)$ needs to be re-computed)
Is it correct to treat $g$ as a well defined (increasing) function?
Thanks, Phanindra