Talk:Extreme value theorem
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I propose the following as an informal introduction:
The extreme value theorem in mathematics is a way of stating that a smooth line has one or more highest and lowest points where no other point is higher than the highest point and no other point is lower than the lowest point. 213.55.136.205 01:28, 14 Dec 2004 (UTC)
[edit] The Boundedness Theorem
I was readig over this and remembered reading Uniform boundedness principle, I'm not sure it's the same theorem. Webhat 08:02, 13 May 2006 (UTC)
[edit] Boundedness is not weaker than having a max/min.
I disagree with the statement that the boundedness theorem is "A weaker version of this[Extreme Value] theorem". Every closed and bounded interval has a maximium and a minimum value, so the Extreme Value Theorem is a consequence of Boundedness--it is because the interval is bounded that we know it has a max/min. So, they are actually the same theorem, but Boundedness is more general--which (in my opinion) makes it stronger, not weaker: if an interval is closed and bounded we know that it has a max/min, but there are other properties of closed and bounded intervals in addition to just having a max/min.
