Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Jussi Piitulainen

Posts: 328
Registered: 12/12/04
Re: Pigeonhole Principle ?
Posted: Oct 7, 2013 2:31 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

shaoyi he <wubuqilai@gmail.com> writes:

> 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?


It's saying there is no way to arrange 0 1 2 3 4 5 6 7 8 9 (3^2 + 1
distinct numbers) so that there is no increasing or decreasing
subsequence of 4 (3 + 1) numbers.

("Strictly" is redundant when the numbers are distinct.)

Checking something:

In 3 1 4 5 9 2 6 8 7 0, there's 1 4 5 9.

In 3 1 5 4 9 2 6 8 7 0, there is no such, so the statement must allow
a subsequence like 3 4 6 7 where the numbers are not adjacent in the
original sequence.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.