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Using Dedekind's notion of the real numbers, show that addition of two Dedekind cuts can be defined easily by S + T = {s + t : s S; t T}.

Using Dedekind's notion of the real numbers, show that addition of two Dedekind cuts

can be defined easily by S + T = {s + t : s ϵ S; t ϵ T}. Verify that S + T is a Dedekind cut  and show that S+T = T+S

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