TITLE: What is this property called for a function? $f(f(x))=f(x)$
QUESTION [15 upvotes]: I am looking for a name for the following types of functions. Suppose that for function f, we have:
$$f(x)=y_x$$ and $$f(f(x))=y_x$$
Is there any name for this property?

REPLY [5 votes]: Idempotent functions
http://en.wikipedia.org/wiki/Idempotence
It is common in computer science, in which you may want the result of an operation to be the same no matter how many times someone performs it. This is especially important in web-apps.
In maths an example would be a projection of a vector into a lower dimensional space.