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Aug 31, 2011 at 15:37 comment added Gerhard Paseman Nope, associativity fails. I guess I had best review my notes on hyperassociativity. Gerhard "Back To The Scratch Pad" Paseman, 2011.08.31
Aug 31, 2011 at 15:32 comment added Gerhard Paseman I haven't checked the details, but I nominate (a term corresponding to) a+a+b+b as a new form of addition. If that works, then there are countably many distinct examples indeed. Gerhard "Ask Me About Quick Guessing" Paseman, 2011.08.31
Aug 31, 2011 at 15:18 history answered Gerhard Paseman CC BY-SA 3.0