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)
“But that beginning was wiped out in fear
The day I swung suspended with the grapes,
And was come after like Eurydice
And brought down safely from the upper regions;
And the life I live now’s an extra life
I can waste as I please on whom I please.”
—Robert Frost (1874–1963)
“What comes over a man, is it soul or mind
That to no limits and bounds he can stay confined?
You would say his ambition was to extend the reach
Clear to the Arctic of every living kind.
Why is his nature forever so hard to teach
That though there is no fixed line between wrong and right,
There are roughly zones whose laws must be obeyed?”
—Robert Frost (1874–1963)