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October 05, 2025, 04:06:42 pm
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Author Topic: MAX?  (Read 4644 times)  Share 

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TrueTears

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Re: MAX?
« Reply #15 on: August 17, 2009, 08:31:25 pm »
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zzdfa

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Re: MAX?
« Reply #16 on: August 17, 2009, 08:32:05 pm »
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key point is that a maximum of a set has to be in the set.
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m@tty

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Re: MAX?
« Reply #17 on: August 17, 2009, 08:38:09 pm »
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So how can a max not exist?

Also this thread may not be of any relevance to the methods board.
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TrueTears

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Re: MAX?
« Reply #18 on: August 17, 2009, 08:44:57 pm »
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I believe zzdfa explained that.
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dcc

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Re: MAX?
« Reply #19 on: August 17, 2009, 08:50:22 pm »
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Quote from: zzdfa on August 17, 2009, 08:32:05 pm
key point is that a maximum of a set has to be in the set.

With the important side-note that said maximum need not exist.
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m@tty

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Re: MAX?
« Reply #20 on: August 17, 2009, 09:01:03 pm »
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Okay.
Under what does a maximum exist?
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TrueTears

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Re: MAX?
« Reply #21 on: August 17, 2009, 09:02:43 pm »
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m@tty

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Re: MAX?
« Reply #22 on: August 17, 2009, 09:20:39 pm »
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I am sorry but I am not understanding this.

This is from the wikipedia article
Quote
A function has a global (or absolute) maximum point at x∗, if f(x∗) ≥ f(x) for all x.
How does this exclude my example?
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Re: MAX?
« Reply #23 on: August 17, 2009, 09:52:26 pm »
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There is no point in the domain which satisfies that condition.

For example, if you let , then something higher would be , and so on. No matter how many '9's you staple on the end of the number there will always be a number with more '9's.
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m@tty

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Re: MAX?
« Reply #24 on: August 17, 2009, 09:58:53 pm »
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OK.
So a maximum does not exist if the domain does not end at a known number?
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TrueTears

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Re: MAX?
« Reply #25 on: August 18, 2009, 04:20:28 pm »
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What max are you talking about?

Local? Global?
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m@tty

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Re: MAX?
« Reply #26 on: August 18, 2009, 04:31:25 pm »
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Global.

Wait I just realised how stupid that was....
Is there no global max in an increasing function? i.e. y=x, where the max would be at the end point.

EDIT: Fixing stupidity
« Last Edit: August 18, 2009, 04:35:55 pm by m@tty »
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TrueTears

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Re: MAX?
« Reply #27 on: August 18, 2009, 04:36:35 pm »
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A function has a global (or absolute) maximum point at x∗, if f(x∗) ≥ f(x) for all x.

If this is not satisfied then the function does not have a global maximum.
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dcc

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Re: MAX?
« Reply #28 on: August 18, 2009, 06:22:24 pm »
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Prove:
A strictly increasing continuous function defined on an open finite interval does NOT possess a maximum point.

DO IT.
« Last Edit: August 18, 2009, 07:04:57 pm by dcc »
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