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

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Graham Cooper

Posts: 4,348
Registered: 5/20/10
Re: Pigeonhole Principle ?
Posted: Oct 8, 2013 6:54 PM
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On Sunday, October 6, 2013 7:55:59 PM UTC-7, 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?



Every list MUST have some increasing/decreasing sublist (although much smaller).

It seems trivially false.


0.11
0.89
0.111
0.889
0.1111
0.8889
..
n^2+1


or as the OP stated, trivially true if re-sorting is allowed.

Herc





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