Let $f$ be monotone ascending (for every $x\le y, ( f(x) \le f(y))$ in the segment $(a,b)$
prove that: $\lim_{x\to x_0^+} f(x) = \inf_{x>x_0} f(x)$
thats the question.
a hint i can use states: if every monotone subsequence of a sequence $x_n$ converges to $x$ so does $x_n$
i couldn't find a connection between the hint and the desired result, any ideas?