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In Munkres' Topology he defines a Cartesian product AxB to be all (a,b) such that a is in A and b is in B. He says that this is a primative way of looking at things. And then defines it to be {{a},{a,b}}
He says that if a = b then {a,b} will just be {a,a} = {a} and therefore will only be {{a}}.
What I don't understand is the the need for {a,b}, why not just define the Cartesian product to be {{a},{b}}. If a = b you get the same result.
He says that if a = b then {a,b} will just be {a,a} = {a} and therefore will only be {{a}}.
What I don't understand is the the need for {a,b}, why not just define the Cartesian product to be {{a},{b}}. If a = b you get the same result.