Bounds of Functions
The definitions can be generalised to sets of functions.
Given a set S of functions with domain F and a partially ordered set as codomain, a function g with domain is an upper bound of S if for each function f in S and for each x in F. In particular, g is said to be an upper bound of f when S consists of only one function f (i.e. S is a singleton). This does not imply that f is a lower bound of g.
Read more about this topic: Upper And Lower Bounds
Famous quotes containing the words bounds of, bounds and/or functions:
“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)
“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)
“One of the most highly valued functions of used parents these days is to be the villains of their children’s lives, the people the child blames for any shortcomings or disappointments. But if your identity comes from your parents’ failings, then you remain forever a member of the child generation, stuck and unable to move on to an adulthood in which you identify yourself in terms of what you do, not what has been done to you.”
—Frank Pittman (20th century)