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Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.
21
votes
Bijection $\varphi:\mathbb{N}\to\mathbb{N}$ that distorts every finite arithmetic progression
It exists for rather trivial reasons. Define this map inductively. In the even steps, send the smallest element of the domain, which does not yet have an image to the smallest element of the range, su …