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answered Intuitive explanation to Probability question
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comment Bound on cardinality of a union
Thanks, this gives a much better estimate; maybe this is all one can reasonably say. As for motivation, an answer to this question gives an upper bound for Ramsey numbers, see the tag. (In some cases it is very close, though not better, than the best known upper bound.)
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accepted Bound on cardinality of a union
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comment Bound on cardinality of a union
This bound might be negative. More generally, if the double intersections all have size N_2 that might force at least some of the triple intersections to be nonempty.
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comment Bound on cardinality of a union
A straightforward application of inclusion-exclusion, ignoring the terms of the wrong sign, gives a lower bound. But it will generally be far from optimal.
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asked Bound on cardinality of a union
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answered (how) are vector bundles and homotopy groups related?
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