As Matt said, I did explain why it is not an error to split an infinitive, but I didn't explain what an infinitive is. So here goes:
An infinitive is the most basic form of a verb. The marker of an infinitive is the word "to." To be, to eat, to dance, to sleep, to go, to play, to know, are all infinitives. These can all be changed into gerunds (the "ing" form of the verb)---being, eating, dancing, sleeping, going, playing, knowing---and they can all be adjusted according to tense---I am/I was; I have eaten/I am eating/I will eat---and so on.
Basically, take any verb and strip it down and you will find the infinitive form.
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