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:
“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)
“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)
“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)