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What are Connes and coworkers talking about: Fun with a field with one element? Also,

I don't have much algebra background but thought a field with 1=0 is degenerate?

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See this MO question, or in fact all of these MO questions. – Zev Chonoles Jul 18 '12 at 2:30
Sometimes it is pretty clear that they make up stuff just to throw people off. – Will Jagy Jul 18 '12 at 3:59

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