Mathematicians often speak of finding necessary and sufficient conditions for some property $P$. But $P$ is a necessary and sufficient condition for $P$. So, how do we determine what a non-trivial necessary and sufficient condition is? Is there a formal and rigorous definition of such a thing?
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No, there is not. This is far too vague to have any universal answer. – lulu Jun 13 '20 at 22:08
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No. Why should there be? $Q$ is a necessary and sufficient condition for $P$ iff $P$ and $Q$ are logically equivalent. It is a value judgement whether the logical equivalence is non-trivial.
Rob Arthan
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