Definition - The non-finite uninflected form of a verb.

Example -
There are two forms:
(1) the bare infinitive (I made him eat the cake), and
(2) the full infinitive (I asked him to eat the cake)

Etymology -
The word derives from the Latin infinitivus, unlimited or indefinite.
Note: Diomedes called the Latin version the infinitivus, because it doesn't have a definite person or number.

Oxford English Dictionary -
Its first citation is from 1520:
"Quis, qui, is … gouerned … somtyme of ye infinytyue mode folowynge."
(Whitinton Vulg. (1527) 3)

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