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
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—William Wordsworth (1770–1850)