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we can find m < n such that a_m <= a_n and b_m <= b_n

Source: 1972 Swedish Mathematical Competition p6

March 26, 2021
algebrainequalities

Problem Statement

a1,a2,a3,…a_1,a_2,a_3,\dots and b1,b2,b3,…b_1,b_2,b_3,\dots are sequences of positive integers. Show that we can find m<nm < n such that am≤ana_m \leq a_n and bm≤bnb_m \leq b_n.
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