If S ⊂ R, then an upper bound for the set S is a number a ∈ R such that s ≤ a for each s ∈ S.

We call a real number y a least upper bound of the set S if (1) y is an upper bound for S and (2) if a is any upper bound for S, then y ≤ a.

See ita-2-3-1-pg23.

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