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