Binary operations | Algebraic properties of elements | Semigroup theory

Absorbing element

In mathematics, an absorbing element (or annihilating 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, with the notable exception: under additive notation zero may, quite naturally, denote the neutral element of a monoid. In this article "zero element" and "absorbing element" are synonymous. (Wikipedia).

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From playlist PHYSICS 66 - QUANTUM MECHANICS

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Related pages

Composition of relations | Extended real number line | Identity element | Null semigroup | Greatest common divisor | Semigroup | Logical disjunction | Empty set | Zero matrix | Mathematics | Set (mathematics) | Integer | Idempotent (ring theory) | Real number | Ring (mathematics) | Semiring | Matrix multiplication | Magma (algebra) | Boolean algebra | Logical conjunction | Matrix (mathematics) | Binary operation | Monoid