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Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.

51 votes

How decreasing can a bijection $f:\mathbb{N}\to\mathbb{N}$ be?

This problem arises in Section 4.3 of my PhD thesis in connection with a Ramsey-type result for infinite tournaments. The answer of $3/4$ is also confirmed by Theorem 4.5 in that section, and the corr …
Alistair Benford's user avatar