Number & MeasureGreek → English
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.