Infinitives are used to indicate purpose or intention, as in "I want to email Billy," or "To get certified, I must pass the licensing test." They can also be used as a noun to present an action as a thing ("To know me is to love me"), but we'll be talking about infinitives used as modifiers (adjectives or adverbs).
You might have heard an old grammar edict: "Don't split the infinitive." That refers to the previous forbidden tactic of inserting an adverb in the middle between the "to" and the verb. (19th Century English grammarians tended to honor Latin grammar rules, and clearly you cannot split a one-word infinitive as exists in Latin.)
As the great grammarian H.W. Fowler commented, "No other grammatical issue has so divided English speakers since the split infinitive was declared to be a solicism in the 19th century: raise the subject of English usage in any conversation today and it is sure to be mentioned." In fact, he divided the entire English-speaking population by their attitudes towards the split infinitive: "Those who don't know and don't care, those who don't know and do care, those who know and approve, those who know and condemn, and those who know and discriminate."
Let's be among those who know and discriminate!
So here's the question. I'm going to give you two famous infinitive quotations, both stately and portentous with meaning. One has the adverb BEFORE the infinitive in a way that even sticklers would approve. One cavalierly splits the infinitive to add an adverb.
Both are correct. Why? Why is each correct when one follows the "rule" and the other doesn't?
Hamlet, the Prince of Denmark:
To be or not to be, that is the question.
James T. Kirk, the Starship Captain:
To boldly go where no man has gone before.
Your turn! What is the difference? Why in the first should the adverb "not" be placed in front of the infinitive "to be", and in the second, the adverb is correctly placed right before the verb? Speculations please!
(Here is a site that discusses Fowler's philosophy: http://www.eng-lang.co.uk/fowler.htm)
(And here's a fun rendition of "to be or not to be"-- A two-year-old playing Hamlet. )