From Teflpedia

An infinitive, is a verb that lacks finiteness, which basically means that either it lacks a subject or it is a subject. It is a type of verbal. There are two infinitives in English; a bare infinitive and a to-infinitive. Somewhat confusingly, either of these may be referred to simply as "the infinitive" without further specification.

Name Example Notes
Bare infinitive He made me do it!
To infinitive I want to go to the park

To complain would show disrespect.

In pedagogic grammar, modal verbs are sometimes said to take a bare infinitive (e.g. "We can do it!"), whereas a better analysis shows that they are followed by an uninflected base form main verb.

In most other European languages, there is only a single infinitive is a single word, e.g. "to play" is "jouer" in French. Hence the prescriptivist split infinitive rule.

Full modal verbs do not have infinitives. For example one cannot say *"to can"; one would have to employ a different way of achieving the same task, e.g. by using "to be able to" or "to be allowed to". See infinitive of a modal verb.