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3 Texified because this question was on the front page anyway

A simple application is the following:

Every sequence of $n^2 +1$ distinct real numbers contains a subsequence of length $n +1$ that is either strictly increasing or strictly decreasing.

(Other simple consequences can be found here.)

2 typesetting

A simple application is the following:

Every sequence of distinct real numbers contains a subsequence of length that is either strictly increasing or strictly decreasing.

(Other simple consequences can be found herhere.)