These two words, which originally had quite distinct meanings, have become so blended together that most people no longer distinguish between them. If you want to avoid irritating the rest of us, use “imply” when something is being suggested without being explicitly stated and “infer” when someone is trying to arrive at a conclusion based on evidence. “Imply” is more assertive, active: I imply that you need to revise your paper; and, based on my hints, you infer that I didn’t think highly of your first draft.
“Impertinent” looks as if it ought to mean the opposite of “pertinent,” and indeed it once did; but for centuries now its meaning in ordinary speech has been narrowed to “impudent,” specifically in regard to actions or speech toward someone regarded as socially superior. Only snobs and very oldfashioned people use “impertinent” correctly; most people would be well advised to forget it and use “irrelevant” instead to mean the opposite of “pertinent.”
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