MathDB

5

Part of 1987 ITAMO

Problems(1)

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

Source: ITAMO 1987 p5

2/2/2020
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.
Sequencealgebrainequalities