\begin{definition}[Definition:Modified Kaprekar Mapping]
The '''modified Kaprekar mapping''' is the arithmetic function $K: \Z_{>0} \to \Z_{>0}$ defined on the positive integers  as follows:
Let $n \in \Z_{>0}$ be expressed in some number base $b$ (where $b$ is usually $10$).
Let $n'$ be the positive integer created by:
:arranging the digits of $n$ into descending order of size
then:
:exchanging the last two digits.
Let $n''$ be the positive integer created by:
:arranging the digits of $n$ into ascending order of size
then:
:exchanging the first two digits.
Then:
:$\map {K'} n = n' - n''$
making sure to retain any leading zeroes to ensure that $\map K n$ has the same number of digits as $n$.
\end{definition}