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.
