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Topic: Pigeonhole Principle ?
Replies: 9   Last Post: Oct 14, 2013 2:15 AM

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quasi

Posts: 10,259
Registered: 7/15/05
Re: Pigeonhole Principle ?
Posted: Oct 6, 2013 11:31 PM
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shaoyi he wrote:
>
>in discrete mathematics and its applications 6th ,in Pigeonhole
>Principle, the author give a THEOREM(page 351):
>
>Every sequence of n^2 + 1 distinct real numbers contains
>a subsequence of length n + 1 that is either strictly increasing
>or strictly decreasing.
>
>i donnot know what's the theorem for? because when we sort the
>n^2 + 1 distinct real numbers, we can get n^2+1 that is either
>strictly increasing or strictly decreasing. so how to
>understand this?


The theorem asserts that without changing the order of the terms,
there is already a strictly increasing or strictly decreasing
subsequence of length n + 1.

quasi



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