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exist different indices r,s such that a_r \ge a_s and b_r \ge b_s, over N

Source: ITAMO 1987 p5

February 2, 2020
Sequencealgebrainequalities

Problem Statement

Let a1,a2,...a_1,a_2,... and b1,b2,..b_1,b_2,... be two arbitrary infinite sequences of natural numbers. Prove that there exist different indices rr and ss such that ar≥asa_r \ge a_s and br≥bsb_r \ge b_s.
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