A monoid is a semigroup whose operation has a neutral element, its identity; a unit of a monoid is an element with a two-sided inverse.
In the setting of Routine Facts, Continued: Typed Arithmetic, Maps and Predicativity, let be a semigroup.
Monoids. is a monoid if has a neutral element. This neutral element, unique by A Binary Operation Has at Most One Neutral Element (i), is the identity of the monoid and is written .
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