Is that a shocker to you?
First, let me explain an infinitive. It’s a verb form in English that uses the word “to” with the root form of the verb. The result, a kind of verbal, is called an infinitive. It can function as a noun, as in “To err is human; to forgive, divine.” There, it’s the subject of each clause. I wrote about two kinds of verbals here. This one, the infinitive, is the one I didn’t cover there. In this post I’m focusing on the false belief that there is such a thing as a “split infinitive.” I’m not explaining the verbal form.
So, all right. We have a two-word formation, like “to lose.” That “to” is not grammatically part of the infinitive. Rather, in Oxford English Grammar Greenbaum calls it a subordinator, while Huddleston/Pullum in their Cambridge Grammar of the English Language prefer “the infinitival to.” The grammatical part is that root form, “lose.” No grammatical rule says that other words can’t come between that “to” and the root form. Some folks in the 19th century got it into their heads, though, to force Latin grammar rules onto English, so we ended up with the specious nonrule against “split infinitives.” But here’s the thing: In Latin (and other languages as well, like French), it’s impossible to “split” an infinitive because that form is a single word. There’s nothing to separate, nowhere to intervene with another word.
Don’t tie yourself into knots trying to keep that “to” with that root verb. It’s not wrong. There’s no rule saying you can’t write “He wanted to just be left alone.” (The question of whether that “just” is worth keeping is a separate one, and I’m not touching it here. One could as easily replace it with “simply,” if that makes it more palatable to the reader.) And if you see it written that way, you’re under no obligation to “correct” it. There’s nothing to correct, from a grammatical standpoint.
If you’re up for a bit of research, I’ll recommend getting your eyes/hands on the aforementioned grammar texts. Personally, I have the student guide version of Cambridge because the full edition was out of my price range. In Greenbaum, the “split infinitive” is relegated to a chapter note in the section at the end of the text. (It didn’t even earn space in the main text. Only a note.)