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

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Posts: 6
Registered: 7/21/13
Pigeonhole Principle ?
Posted: Oct 6, 2013 10:55 PM
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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?

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