# Absorbing element

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In algebra, an absorbing element or a zero element for a binary operation has a property similar to that of multiplication by zero.

Formally, let ${\displaystyle \star }$ be a binary operation on a set X. An element O of X is absorbing for ${\displaystyle \star }$ if

${\displaystyle O\star x=O=x\star O\,}$

holds for all x in X. An absorbing element, if it exists, is unique.