The question is that which one is correct and why, one sentence is " she is a lot of fun to be with." another one is "she has a lot of fun to be with."
"she is a lot of fun to be with " is the correct one
A mistake I hear English speakers make is "It was so fun," instead of saying "It was so much fun," as if the word 'fun' is an adjective, instead of a noun.
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A mistake I hear English speakers make is "It was so fun," instead of saying "It was so much fun," as if the word 'fun' is an adjective, instead of a noun.

?? At least in my dialect, which is close to General American, "fun" is both an adjective and a noun (and, rarely, even a verb), and "It was so fun" is perfectly grammatical.

Jim Heckman
Sorry, Jim. When I hear that, it sounds like a wrong note played on a piano. I grimace when I hear it and I would NEVER teach it. The only way I'd use it as an adjective: It was a fun evening. Americans - I notice on TV - are destroying the language. For example, I keep hearing "There's a lot of things I like." Eeuuww!
I heard "extremely capable" today. This doesn't happen often, but it did bother me a little. Capable, to me, is a finate state. Either one is or one is not capable. Once that state is exceeded, one is still merely capable.
Am I wrong to let this bother me?
BTW, I've been speaking English my whole life and fun is indeed an adjective. Just because a usage is informal does not make it incorrect. Languages do, in fact, evolve and new words are added to the dictionaries every year. Dialects, I would argue, are unique even within specific households. To argue against that is to argue that you're the best cat-herder there ever was.
"I was just funning you," however colloquial, has a distinct meaning within it's dialect and to those who speak and understand it. So, it can be a verb as well.
Certainly you wouldn't want to teach it to those learning English as a second language, however, it is no less correct.
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