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)
““All men live in suffering
I know as few can know,
Whether they take the upper road
Or stay content on the low....””
—William Butler Yeats (1865–1939)
“Firmness yclept in heroes, kings and seamen,
That is, when they succeed; but greatly blamed
As obstinacy, both in men and women,
Whene’er their triumph pales, or star is tamed —
And ‘twill perplex the casuist in morality
To fix the due bounds of this dangerous quality.”
—George Gordon Noel Byron (1788–1824)