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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—Henry David Thoreau (1817–1862)
“How far men go for the material of their houses! The inhabitants of the most civilized cities, in all ages, send into far, primitive forests, beyond the bounds of their civilization, where the moose and bear and savage dwell, for their pine boards for ordinary use. And, on the other hand, the savage soon receives from cities iron arrow-points, hatchets, and guns, to point his savageness with.”
—Henry David Thoreau (1817–1862)
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