Unless "know" means something different from my intuitive notion, it is not at all clear (and in fact false) that S is a subset of K(K(S)). Let S be the singleton containing President Obama. Then K(S) is a very large subset, and I suspect K(K(S)) is empty. Are you somehow assuming that if A knows B then B knows A? --ms On 1/27/2011 1:48 PM, James Propp wrote:
I'm thinking of submitting the following bit of silliness to Mathematics Magazine: http://jamespropp.org/galois.pdf Comments are welcome!
In particular, I'm pretty sure that statements fairly close to "The people you know are the people who know all the people who know all the people you know" already occur in print, and I'd like to give credit where credit is due (even if that prevents my article from fitting onto one page).
Jim Propp
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