If an operation * is defined on a set E, then

*a*is an absorbing element of the operation * if and only if*x * a = a*for all*x*in E.### Example

The whole number 0 is the absorbing element for the operation of multiplication on the set of real numbers :

3 × 0 = 0 × 3 = 0

0 × 3.5 = 3.5 × 0 = 0