Lately I have been trying to prove the extreme value theorem using the concept of Cauchy sequences but I can't figure out how to start or where to go after I have started, and I was if anyone could lead me to proving it.
Theorem:
In calculus, the extreme value theorem states that if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain a maximum and a minimum, each at least once.