The verb ought is sometimes excluded from the class of auxiliaries (specifically the modal auxiliaries) on the grounds that, unlike the principal modals, it requires the to-infinitive rather than the bare infinitive.
The will/shall future consists of the modal verb will or shall together with the bare infinitive of the main verb, as in "He will win easily" or "I shall do it when time permits".
For a command, take the imperative form of the conjugated verb from the infinitive and put it at the beginning of the sentence followed by the corresponding personal pronoun.
The perfect infinitive can further be governed by modal verbs to express various meanings, mostly combining modality with past reference: "I should have eaten" etc.
The bare infinitive is used as complement of the dummy auxiliary do, most modal auxiliary verbs, verbs of perception such as see, watch and hear (after a direct object), and the verbs of permission or causation make, bid, let, and have (also after a direct object).
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For example, in German, the infinitive form of the verb usually goes to the end of its clause, whereas a finite verb (in an independent clause) typically comes in second position.
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This applies to the modal verbs (can, must, etc.), as well as certain related auxiliaries such as the had of had better and the used of used to.
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In many other languages the infinitive is a single word, often with a characteristic inflective ending, such as manger ("(to) eat") in French, portare ("(to) carry") in Latin, lieben ("(to) love") in German, etc.
The split infinitive, specifically its famous use in the Star Trek opening sequence, is the basis of a joke from Douglas Adams' The Hitchhiker's Guide to the Galaxy: "In those days men were real men, women were real women, small furry creatures from Alpha Centauri were real small furry creatures from Alpha Centauri. And all dared to brave unknown terrors, to do mighty deeds, to boldly split infinitives that no man had split before — and thus was the Empire forged."