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Absorbing element
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, an absorbing element (or annihilating element) is a special type of element of a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> with respect to a <a href="/facts/Binary_operation/CYtow0bz">binary operation</a> on that set. The result of combining an absorbing element with any element of the set is the absorbing element itself. In <a href="/facts/Semigroup/rgSdk2kt">semigroup</a> theory, the absorbing element is called a <a href="/facts/Semigroup/rgSdk2kt">zero element</a> because there is no risk of confusion with <a href="/facts/Zero_element/PvH2qhxh">other notions of zero</a>, with the notable exception: under additive notation <i>zero</i> may, quite naturally, denote the neutral element of a monoid. In this article "zero element" and "absorbing element" are synonymous. </p>