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.

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

Both theorems need the completeness axiom of the reals. They also provide an existence for a limit of a certain Cauchy sequence. So they will be equivalent to the completeness axiom.


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