supremum

Noun

Meaning

supremum (plural suprema)

English Wikipedia has an article on:supremumWikipedia (set theory) (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.

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Examples

A set A of real numbers (blue balls), a set of upper bounds of A (red diamond and balls), and the smallest such upper bound, that is, the supremum of A (red diamond). Source: Internet

As a linear continuum The order on the number line Each set on the real number line has a supremum. Source: Internet

By analogy with the above, in the domain of the extended reals, negative infinity is the identity element for the maximum and supremum operators, while positive infinity is the identity element for minimum and infimum. Source: Internet

Although is also an upper bound, it is not the "least upper bound" and hence is not the "supremum". Source: Internet

Consequently, the supremum is also referred to as the least upper bound (or LUB). Source: Internet

Definition A real set with upper bounds and its supremum. Source: Internet

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