5. Show that in any row of mn + 1 distinct real numbers there is either an increasing subsequence of length (at least) m + 1 or a decreasing subsequence of length (at least) n+ 1. Notes: subsequences need not consist of consecutive elements of the row. Eg. The row of 7 numbers: 6, 5, 1, 9, 3, -4, 13/2, has (longest) increasing subsequence (1, 3, 13/2) and (longest) decreasing subsequence (6,5, 3, -4), for m = 3, n = 2.
5. Show that in any row of mn + 1 distinct real numbers there is either an increasing subsequence of length (at least) m + 1 or a decreasing subsequence of length (at least) n+ 1. Notes: subsequences need not consist of consecutive elements of the row. Eg. The row of 7 numbers: 6, 5, 1, 9, 3, -4, 13/2, has (longest) increasing subsequence (1, 3, 13/2) and (longest) decreasing subsequence (6,5, 3, -4), for m = 3, n = 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you please do question 5?thanks
Transcribed Image Text:of speed, angular speed and motion in the absence of a force
(c) My revised/clarified version is less ambiguous, generalized, and employs SI units.
5. Show that in any row of mn + 1 distinct real numbers there is either an increasing
subsequence of length (at least) m + 1 or a decreasing subsequence of length (at least)
n+ 1. Notes: subsequences need not consist of consecutive elements of the row. Eg.
The row of 7 numbers: 6, 5, 1, 9, 3, -4, 13/2, has (longest) increasing subsequence
(1, 3, 13/2) and (longest) decreasing subsequence (6,5, 3, -4), for m = 3, n = 2.
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