An infinitive is the “core” of a verb, meaning it can exist independently, or in abstraction.
“To go,” for example, is an infinitive; an abstract concept. But “going” isn’t, since “going”
implies context: You are always going to something.
In Latin, infinitives are one word: “to go,” for instance, is “ire” in Latin. It therefore can’t be
split.
In English, however, you can split the infinitive (to boldly go).
Coote’s affinity for Latin made him decide that split infinitives aren’t grammatically
“proper.”