Every verb has a base infinitive form. We think of the infinitive as the verb with the preposition to in front of it: as in to have, to hold, to love, to honor, to cherish. Infinitives appear in the language in three ways: (1) they appear alone to show some of the tenses, as in I write, You write, We write, They write; (2) they join auxiliary verbs to form other tenses or conditions, as in I will write, He could write; and (3) they are used to form infinitive phrases, which can act as nouns, adjectives, or adverbs. The term infinitive phrase is elsewhere defined.
Controversy rages over whether you may split an infinitive by putting other words between the to and the infinitive verb. The short answer is yes. The so-called rule against split infinitives is simply not a rule. For a thorough discussion and a press release by the Oxford English Dictionary, study the section on Verbs in Parts of Speech on Grammar.com.
The following, which appear in New Fowler, are correct:
That's when you have to really watch yourself. —Quarto, 1981 (UK).
It led Cheshires to finally abandon publishing fiction at all. —B. Oakley, 1985 (Australia).
The goal is to further exclude Arafat. —U.S. News & World Report, 1986 (United States).