PROOF. Let SI and S2 be suprema of the same set E. Then both SI and S2

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PROOF. Let SI and S2 be suprema of the same set E. Then both SI and S2 are upper bounds of E, whence by Definition 1. 16iii, SI :::; S2 and S2 :::; SI. We conclude by the Trichotomy Property that s 1 = S2·

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