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The infinitive is the most 'basic' form of a verb. For example: 'to run' or 'to sing' or 'to be'. These words are 'unconjugated' because they don't have a subject changing the spelling.
English language has three non-finite verbal forms, but by long-standing convention, the term "infinitive" is applied to only one of these. (The other two are the past- and present-participle forms, where the present-participle form is also the gerund form.) In English, a verb's infinitive is its unmarked form, such as be, do, have, or sit, often introduced by the particle to. When this particle is absent, the infinitive is said to be a bare infinitive; when it is present, it is generally considered to be a part of the infinitive, then known as the full infinitive (or to-infinitive), and there is a controversy about whether it should be separated from the main word of the infinitive (see Split infinitive). Nonetheless, modern theories typically do not consider the to-infinitive to be a distinct constituent, instead taking the particle to for operating on an entire verb phrase; so, to buy a car is parsed as to [buy [a car]], not as [to buy] [a car].
The bare infinitive and the full infinitive are mostly in complementary distribution. They are not generally interchangeable, but the distinction does not generally affect the meaning of a sentence; rather, certain contexts call almost exclusively for the bare infinitive, and all other contexts call for the full infinitive.
Huddleston and Pullum's Cambridge Grammar of the English Language (CGEL), published in 2002, does not use the notion of the infinitive, arguing that English uses the same form of the verb, the plain form, in infinitival clauses that it uses in imperative and present-subjunctive clauses.