Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 130 / 1 / b / Solution

Restrict the given finite edge-colouring to the positive integers inside $\mathbb{Q}$. The infinite Ramsey theorem gives an infinite monochromatic subset; listing it in increasing order producesApply the same theorem separately to the negative integers. If the selected indices satisfy $n_1<n_2<\cdots$, thenforms a monochromatic set with $y_1>y_2>\cdots$. The two monochromatic colours need not agree.

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