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 lower, upper and, upper and/or bounds:
“Upper and Lower Kingdom will declare
God’s in this wooden toy,
no less
than where
great Taurus ploughs his course.”
—Hilda Doolittle (1886–1961)
“Upper and Lower Kingdom will declare
God’s in this wooden toy,
no less
than where
great Taurus ploughs his course.”
—Hilda Doolittle (1886–1961)
“The enemy are no match for us in a fair fight.... The young men ... of the upper class are kind-hearted, good-natured fellows, who are unfit as possible for the business they are in. They have courage but no endurance, enterprise, or energy. The lower class are cowardly, cunning, and lazy. The height of their ambition is to shoot a Yankee from some place of safety.”
—Rutherford Birchard Hayes (1822–1893)
“Nature seems at each man’s birth to have marked out the bounds of his virtues and vices, and to have determined how good or how wicked that man shall be capable of being.”
—François, Duc De La Rochefoucauld (1613–1680)