Upper and Lower Bound

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A Upper and Lower Bound are the limits of a set, subset or a function .



References

2015

Bounds of functions, The definitions can be generalized to functions and even sets of functions. Given a function f with domain D and a partially ordered set (K, ≤) as codomain, an element y of K is a upper bound of f if yf(x) for each x in D. The upper bound is called sharp if equality holds for at least one value of x.
Function g defined on domain D and having the same codomain (K, ≤) is an upper bound of f if g(x) ≥ f(x) for each x in D.
Function g is further said to be a upper bound of a set of functions if it is an upper bound of each function in that set.
The notion of lower bound for (sets of) functions is defined analogously, with ≤ replacing ≥.

1999