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Number & MeasureGreekEnglish

Monoid

/ˈmɒnɔɪd/noun

A set with an associative operation and an identity element, and no further requirements.

The Greek roots

μόνος
mónos
single, alone
+
εἶδος
eîdos
form, kind

Literally: single-form thing

The story of the word

Strings under concatenation make one, with the empty string as the identity, which is why functional programmers keep bumping into the word. The name is twentieth-century algebra, French monoïde in the Bourbaki circle before it reached English. Drop the identity and you have a semigroup; add inverses and you have a group, so the monoid is the middle rung of a very short ladder.

How it travelled
Ancient Greek → French → English
First recorded
20th century

Same family

monadmonolithasteroidmonotype

In a sentence

Lists form a monoid under append, with the empty list doing nothing when you add it.

Built on the same root

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