The infinitive is a verb with "to" before it. The following sentences contain an infinitive verb:
1. We will have to leave early because it will be busy on the roads at that time of day.
2. I will give you a lift this morning but you will have to walk home this afternoon.
If you put any word between the "to" and the other part of the verb, you have split the infinitive. The following sentences contain split infinitives:
3. You will need to carefully walk between the pots because they tip over easily.
4. He has promised to definitely come before 8 o'clock.
Some people object to split infinitives very strongly, but it can be neater to use one than to avoid it. For example:
5. It is impossible to quietly enter the administration block by the St John's Street entrance late at night.
I think that this split infinitive is preferable to the alternative of putting "quietly" at the end of the sentence where it would be separated by so many words from "enter", the word it describes. There are traditionalists who would not agree with me.
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