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> if you can't remember the boundary conditions they hold under.

At the outskirts of one's knowledge this is inevitably the case. My impression it is still useful to know that a certain implication is possible - and one can look up the exact conditions.



This is why I said operationalizing: you need to memorize enough to either be able to know what to look up, or know it outright if you need to be fast(er).




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