# Is the Bolzano-Weistrass theorem the same as as the Extreme Value Theorem?

I know the theorems do not state exactly the same thing, but, are they stating the same thing in general?

BW Theorem: A bounded sequence of real numbers has a convergent subsequence.

EV 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.

• They are different but for the real numbers a consequence of each other – marwalix May 17 '15 at 9:24
• @marwalix Thanks a lot, that's exactly what I was looking for. – Reinhild Van Rosenú May 17 '15 at 9:44