I've learned recently that the word
"informal" has a fairly positive connotation, that is ...
# Characteristic of or suitable, appropriate to ordinary, casual or familiar use.
# Being more appropriate for use in the spoken language than in the written language.
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Dear Goodman, I agree that
I wish I were is correct and formal, there's no question about it, but ... your primary source (EnglishClub.com) also says
I wish I was form "is possible in
informal, familiar conversation."
There's no need to get excited.... is it?