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.