Student or Learner
I frequently see "to not" instead of "not to" which seems grammar-wise incorrect, but is it acceptable or do they make such a mistake knowing it's wrong?
ex)He did his best to not lose the game.
The 'rule' about splitting infinitives is one that is both widely ignored by speakers and very disputed- it is one of those prescriptions that can raise the temperature of a discussion. With such cases, there is always the trusty fall-back of recommending that people don't do it in formal language.
With a negative, I would generally use not to, but when I want to give extra emphasis or suggest volition, I sometimes reverse the order- if there's no reason for doing it, then I don't. Other people may handle things differently. I am not convinced it's a very helpful rule because it is so widely broken that it is hard to show that it exists- students who are taught it will go outside the classroom and find it broken every day by native speakers.