Definition
Formally, let (S, ∘) be a set S with a binary operation ∘ on it (known as a magma). A zero element is an element z such that for all s in S, z∘s=s∘z=z. A refinement are the notions of left zero, where one requires only that z∘s=z, and right zero, where s∘z=z.
Absorbing elements are particularly interesting for semigroups, especially the multiplicative semigroup of a semiring. In the case of a semiring with 0, the definition of an absorbing element is sometimes relaxed so that it is not required to absorb 0; otherwise, 0 would be the only absorbing element.
Read more about this topic: Absorbing Element
Famous quotes containing the word definition:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)