Can someone explain the setup of the 0=1 exercise? It's poorly worded. Is it saying find: (Y,1,+,1,×) or is it saying find what "1" has to be to make it a valid field?
I don't remember the precise proof, but if memory serves it derives from the existance of opposites and inverses, and 0 and 1 being unique in the set, due the commutative properties of abelean groups.