So I was wondering, is there a name for a function whose output is always less than or equal to its input ($f(x)≤x$)? I know there is a name for functions that satisfy $x_1
Terminology for properties of functions.
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functions
terminology
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0A function satisfying "$x_1
" is called *strictly increasing*, not *monotonic*. – 2011-12-13 -
1I've seen functions satisfying "$x \le f(x)$" called *inflationary*, *progressive*, or *extensive*. Thus one could use *deflationary* or *regressive* for your property, but I haven't actually seen such usage. – 2011-12-13
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0In mathematics, a monotonic function (or monotone function) is a function that preserves the given order: http://en.wikipedia.org/wiki/Monotonic_function. Oh and thanks for your comment. :) – 2011-12-13