Greatest Lower Bound

Let S be a nonempty set of real numbers that has a lower bound. A number c is the called the greatest lower bound (or the infimum, denoted infS) 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 a lower bound for S, then k<=c.

See also

Infimum, Infimum Limit, Least Upper Bound, Limit, Lower Bound, Meet

Portions of this entry contributed by Lik Hang Nick Chan

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

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Greatest Lower Bound

Cite this as:

Chan, Lik Hang Nick and Weisstein, Eric W. "Greatest Lower Bound." From MathWorld--A Wolfram Web Resource.

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