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Is there a name for a function which, when applied to its own result, will always return that same result?

e.g. for a function $f(x) = ||x||$

$f(2.5) = 2$

and

$f(f(2.5)) = 2$

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    The property is [Idempotence](https://en.wikipedia.org/wiki/Idempotence). – 2017-01-09
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    @MauroALLEGRANZA post this as answer for me to mark as correct – 2017-01-09

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I would say that the common name is idempotent, see https://en.wikipedia.org/wiki/Idempotence