1
$\begingroup$

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 (monotonic) so I figured there would be a name for $f(x)≤x$. Does anyone know what it is? A good example of this would be the greatest integer function $\lfloor x\rfloor$. Thank you.

  • 0
    A function satisfying "$x_1" is called *strictly increasing*, not *monotonic*.2011-12-13
  • 1
    I've seen functions satisfying "$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
  • 0
    In 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

1 Answers 1