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Least Upper Bound

  • Definition: Let S be a nonempty set of real numbers that has an upper bound. Then a number c is called the least upper bound (or the supremum, denoted sup S) for S if and only if it satisfies the following properties: 1. c>=x for all x in S. 2. For all real numbers k, if k is an upper bound for S, then k>=c.

    Source: http://mathworld.wolfram.com

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