The identity function
is the function
which assigns every real number
to the same real number
. It is identical to the identity
map.
The identity function is trivially idempotent, i.e., .
The identity function
in the complex plane is illustrated above.
A function that approximates the identity function for small to terms of order
is given by
 |
(OEIS A115183 and A115184). This function leads to some nice pi approximations.