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?
Given the field (Y, 0, +, 1, *), you need to show that either 0 != 1, or 0 = 1 is the only element in the set.
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.
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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?
Given the field (Y, 0, +, 1, *), you need to show that either 0 != 1, or 0 = 1 is the only element in the set.
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.