Upper and lower bounds

In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (K, ≤) is an element of K which is greater than or equal to every element of S. The term lower bound is defined dually as an element of K which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound. The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds.

单词	Upper and lower bounds
释义	Upper and lower bounds 英语百科 Upper and lower bounds In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (K, ≤) is an element of K which is greater than or equal to every element of S. The term lower bound is defined dually as an element of K which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound. The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds.
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