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.
Read more about Upper And Lower Bounds: Properties, Examples, Bounds of Functions
Famous quotes containing the words upper and/or bounds:
“If the upper beams are not straight, the lower beams will be crooked.”
—Chinese proverb.
“Prohibition will work great injury to the cause of temperance. It is a species of intemperance within itself, for it goes beyond the bounds of reason in that it attempts to control a mans appetite by legislation, and makes a crime out of things that are not crimes. A Prohibition law strikes a blow at the very principles upon which our government was founded.”
—Abraham Lincoln (18091865)