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Have you actually looked at and analyzed the handful of search results for shan’t in the BYU Corpus of American English?
If you had an ESL student who was preparing to live and work in the US, what would your advice to him/her be with respect to using the word shan’t? From what you’ve written, it seems you’d either simply say “Some Americans use the word shan’t.” or you would simply start spewing various search numbers rather than mentioning context or register. Would you even bother to mention, for example, that some of the search results in American media are excerpts of things written by people whose mother tongue is not English and who have never lived in the US?
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I’d advise them to ask just where and when it is used, for what purposes, and by whom. And I’d get the person below to tell me who exactly “us” means:
Let me ask you a similiar question: If you had an ESL student who was preparing to live and work as a writer, journalist, or similar, in the US, or one who was planning to study American literature, in the US, what would your advice to him/her be with respect to using the word shan’t?