# Absorbing Element

In mathematics, an absorbing element is a special type of element of a set with respect to a binary operation on that set. The result of combining an absorbing element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a zero element because there is no risk of confusion with other notions of zero. In this article the two notions are synonymous. An absorbing element may also be called an annihilating element.

### Other articles related to "absorbing element, absorbing elements":

Absorbing Element - Examples
... The most well known example of an absorbing element in algebra is multiplication, where any number multiplied by zero equals zero ... Zero is thus an absorbing element ... It is absorbing element for every operation, ie ...
List Of Zero Terms - Absorbing Elements
... An absorbing element in a multiplicative semigroup or semiring generalises the property 0 × x = 0 ... Examples include The empty set, which is an absorbing element under Cartesian product of sets, since {} × S = {} The zero function or zero map, defined by z(x) = 0, under ... Many absorbing elements are also additive identities, including the empty set and the zero function ...

### Famous quotes containing the words element and/or absorbing:

All forms of beauty, like all possible phenomena, contain an element of the eternal and an element of the transitory—of the absolute and of the particular. Absolute and eternal beauty does not exist, or rather it is only an abstraction creamed from the general surface of different beauties. The particular element in each manifestation comes from the emotions: and just as we have our own particular emotions, so we have our own beauty.
Charles Baudelaire (1821–1867)

An innocent man is a sin before God. Inhuman and therefore untrustworthy. No man should live without absorbing the sins of his kind, the foul air of his innocence, even if it did wilt rows of angel trumpets and cause them to fall from their vines.
Toni Morrison (b. 1931)