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Least Upper Bound

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 supS) for S iff 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.

See also

Greatest Lower Bound, Limit, Supremum, Supremum Limit, Upper Bound

Portions of this entry contributed by Lik Hang Nick Chan

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References

Rudin, W. Principles of Mathematical Analysis, 3rd ed. New York: McGraw-Hill, p. 4, 1976.

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Least Upper Bound

Cite this as:

Chan, Lik Hang Nick and Weisstein, Eric W. "Least Upper Bound." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LeastUpperBound.html

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