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:
“Prohibition will work great injury to the cause of temperance. It is a species of intemperance within itself, for it goes beyond the bounds of reason in that it attempts to control a man’s appetite by legislation, and makes a crime out of things that are not crimes. A Prohibition law strikes a blow at the very principles upon which our government was founded.”
—Abraham Lincoln (1809–1865)
“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)
“The English masses are lovable: they are kind, decent, tolerant, practical and not stupid. The tragedy is that there are too many of them, and that they are aimless, having outgrown the servile functions for which they were encouraged to multiply. One day these huge crowds will have to seize power because there will be nothing else for them to do, and yet they neither demand power nor are ready to make use of it; they will learn only to be bored in a new way.”
—Cyril Connolly (1903–1974)