Decreasing function
A function defined on a set
of real numbers such that the condition
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implies
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Sometimes such a function is called strictly decreasing and the term "decreasing function" is applied to functions satisfying for the indicated values only the condition
(a non-increasing function). Every strictly decreasing function has an inverse function, which is again strictly decreasing. If
is a left-hand (respectively, right-hand) limit point of
,
is non-increasing and if the set
is bounded from above (respectively,
is bounded from below), then for
(respectively,
),
,
has a finite limit; if the given set is not bounded from above (respectively, from below), then
has an infinite limit, equal to
(respectively,
).
Comments
A function such that
is decreasing is called increasing (cf. Increasing function).
Decreasing function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Decreasing_function&oldid=46596