A Simple Proof of Hindman's Theorem
Henry Towsner · arXiv (Cornell University) · 2009
We give a short, explicit proof of Hindman’s Theorem that in every finite coloring of the integers, there is an infinite set all of whose finite sums have the same color. Building on the observation that two of the existing proofs, those by Baumgartner and Galvin-Glazer, have similar divisions of the proof into two stages, we give a proof similar to Hindman’s original argument, but with an analogous two stage construction. 1