# Definition:Reversal

## Definition

Let $m = \sqbrk {a_n a_{n - 1} a_{n - 2} \ldots a_2 a_1 a_0}$ be an integer expressed in base $10$.

That is:

$m = \displaystyle \sum_{k \mathop = 0}^n a_k 10^k$

Its reversal $m'$ is the integer created by writing the digits of $m$ in the opposite order:

$m' = \sqbrk {a_0 a_1 a_2 \ldots a_{n - 2} a_{n - 1} a_n}$

That is:

$m' = \displaystyle \sum_{k \mathop = 0}^n a_{n - k} 10^k$

## Also known as

Some sources use reverse.

Some sources use the term mirror.

## Also see

• Results about reversals can be found here.