This article is from the alt.usage.english FAQ, by Mark Israel misrael@scripps.edu with numerous contributions by others.
We get frequent complaints about the occurrence of "of" in
unedited prose where the meaning is "have". "Have" contracts to
"'ve", so "could've", "might've", "must've", "should've",
"would've", etc. (and their negatives, "couldn't've", etc.), should
be so spelled. People have testified that it's got beyond a
spelling mistake: they've heard "would of" spoken with a clear
pause between the words.
WDEU says: "The OED Supplement dates the naive (or ignorant) use
of "of" back to 1837. [...Y]ou had better avoid it in your own
writing. [...] Bernstein 1977 allows that a schoolchild cannot be
blamed for "could of" -- once."
 
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