Some #thirdsday reading: Division By Three
arxiv.org/abs/math/06057…
"We prove without appeal to the Axiom of Choice that for any sets A and B, if there is a one-to-one correspondence between 3xA and 3xB then there is a one-to-one correspondence between A and B."

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In reply to @christianp

And I feel this is also in the spirit of #thirdsday: What to do When the Trisector Comes, by Underwood Dudley
web.mst.edu/~lmhall/WhatTo…