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sup, the least upper bound of a set, which need not belong to the set.
Also known as: Sup, Least upper bound, LUB
The supremum is the smallest number that nothing in the set exceeds. It differs from the maximum in exactly one way and it is the way that matters: the open interval up to 1 has supremum 1 and no maximum at all, because 1 is not in it.
Denotes the least upper bound of a set of real numbers.
Contexts: Mathematics
Differs from a maximum in that it need not be an element of the set; every maximum is a supremum and not conversely.
Contexts: Mathematics
Always exists for a non-empty set bounded above, which is the completeness property of the real numbers.
Contexts: Mathematics
The three lowercase letters s, u and p in roman type, followed by a set or an expression.