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Math and science::Analysis::Tao::05. The real numbers

Supremum

Let E be a subset of R. If E is not empty and has some upper bound, we define sup(E) to be [...].

We introduce two new symbols, +∞,−∞, to deal with two special cases. If E is non-empty and [...], we set sup(E):=+∞; if E [...], we set sup(E):=−∞.

We refer to sup(E) as the supremum of E, and denote it as sup E.