The Pigeonhole Principle Explained | Built In
The Pigeonhole Principle Explained | Built In
Oct 9, 2023
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SOLVED:A proof of Theorem 3 based on the generalized pigeonhole principle is outlined in this exercise. The notation used is the same as that used in the proof in the text. a) Assume that ik ≤n for k=1.2, …. n^2+1 . Use the generalized pigeonhole principle to show that there are n+1 terms ak1, ak2, …, ak+1 with ii1=ik2=⋯=ihe+1 . where 1 ≤k1<k2 <⋯<kn+1 b) Show that ak j>aki+1 for j=1,2, …, n. [Hint: Assume that ab,<ai j+1 and show that this implies that ih2>ikj, 1. which is a contradiction.] c) U
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