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I'm sorry if I made it worse, but it seems to me that whether the sets consist of positive integers or other elements is not a big difference, since one can take bijections. On the other hand, it would be nice if the statement has a mathematically correct interpretation. Of course, if you want to
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It currently says: "if F is a family of sets with n distinct elements" - what has n distinct elements? The family F? Each of the sets in F? Neither interpretation makes sense. Moreover, even if they did, there should not be two interpretations to choose from. And indeed, the correct statement is
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Would you say it's not a big difference to express all counting problems as being about counting sheep, because anything else can be counted by putting it in bijection with a flock of sheep? —
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Your "correction" made it worse. You made it state that it only applies to sets whose elements are the positive integers from 1 to n. That is ridiculously and unnecessarily restrictive. —
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different from either, and hard to guess from what is written here. (Namely, the union of the sets in F should have n elements).
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worry about which sets are in bijection with ordinals, that would be a reason to object. Is it that?
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