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/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)
“Surely you wouldn’t grudge the poor old man
Some humble way to save his self-respect.
He added, if you really care to know,
He meant to clear the upper pasture, too.”
—Robert Frost (1874–1963)
“How far men go for the material of their houses! The inhabitants of the most civilized cities, in all ages, send into far, primitive forests, beyond the bounds of their civilization, where the moose and bear and savage dwell, for their pine boards for ordinary use. And, on the other hand, the savage soon receives from cities iron arrow-points, hatchets, and guns, to point his savageness with.”
—Henry David Thoreau (1817–1862)