Ask about the extreme value theorem. [closed]

real-analysis

https://www.slideserve.com/gaerwn/extreme-value-theorem

On the fifth slide, an "example 1" is shown where the question is about consistency with the extreme value theorem. We see that in this example there is an absolute maximum and an absolute minimum; however the interval is semi-open. How could this happen if the theorem guarantees the existence of maximum and minimum as long as the interval is closed?


Extreme value theorem is stated for closed intervals. I.e. for a closed intervals, an absolute maximum and an absolute minimum exist.

It does not say that there is no absolute maximum when it is not a closed intervals.

There is no contradiction.

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