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supremum

UK
/suːˈpriːməm/
US
/suˈpriməm/

Translations

supremumnoun
suprema
pl
UK
/suːˈpriːməm/
US
/suˈpriməm/
The supremum of the set is the smallest upper bound.
Супремум множества — это наименьшая верхняя граница.
Synonyms
maximum
upper bound
greatest element
least upper bound
supremumadjective
UK
/suːˈpriːməm/
US
/suˈpriməm/
Used attributively before another noun in mathematical contexts (e.g., "supremum norm").
Synonyms
supreme
paramount
preeminent
sovereign
highest
ultimate
foremost
dominant
predominant
principal

Definitions

supremumnoun
The least upper bound of a set in mathematics, particularly in the context of real numbers, where it is the smallest number that is greater than or equal to every number in the set.
In the set of numbers {1, 2, 3}, the supremum is 3.
More generally, in order theory, the least element among the upper bounds of a subset of a partially ordered set.
In any lattice, the supremum of elements a and b is written a ∨ b.
supremumadjective
Relating to or involving a supremum; based on the least upper bound.
The supremum metric measures the maximum distance between two functions.
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