look through somebody/something (phrasal verb)
to not notice or pretend not to notice someone you know, even though you see them
ldoceonline.com/dictionary/look_1
look through sb
to not notice someone that you know, or to pretend that you have not noticed someone, even though you are looking directly at them
dictionary.cambridge.org/define. … 2+0&dict=P
Why use “to not V”? Why not use “not to V”?
What’s the difference in meaning or style between the above two structures?
You’re supposed to use “not to V”. “To not V” would be ungrammatical in speech or writing.
Both “to not + verb” and “not to + verb” are correct grammatically, but the choice between them depends on the specific context and the emphasis you want to convey. “I try not to hurt you” emphasizes the action of trying, while “I try to not hurt you” emphasizes the action of not hurting. Both are correct, but the first one is more commonly used. Similarly, “I know what not to do” emphasizes the knowing, while “I know what to not do” emphasizes the action of not doing. Again, both are correct, but the first one is more commonly used. In general, “to not + verb” is more commonly used in everyday language, but both forms are grammatically correct and can be used depending on the emphasis you want to convey in your sentence.
https://www.quora.com/When-do-we-use-to-not-verb-or-not-to-verb-Should-I-say-I-try-not-to-hurt-you-or-I-try-to-not-hurt-you-I-know-what-to-not-do-or-I-know-what-not-to-do#:~:text=Both%20are%20correct%2C%20but%20the,one%20is%20more%20commonly%20used.
Both “not to V” and “to not V” are grammatical.
https://www.usingenglish.com/forum/threads/not-to-v-to-not-v.284236/