Confirmation Of A's And I's Please
Crosswords1 min ago
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For more on marking an answer as the "Best Answer", please visit our FAQ.You cannot define a phrase by breaking down the mechanical parts. That barely scratched the surface!
Apropos of nothing means more than simply "off topic" or "irrelevant" Those are merely denotative aspects of the phrase.
The connotative aspect of the phrase suggests that whatever you are claiming as "apropos of nothing" is not only irrelevant, it is of no value. It does not edify you in any way and probably makes you a trifle dumber for knowing it.
See the novel Sir Apropos of Nothing for an interesting read about a character that embodies the multiple dimensions of this singular phrase.