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May 3, 2019 at 6:04 comment added dvitek The number of lines that have either one or two points in $F$ is exactly $|F|*(|V|-|F|)$, so the sum of (b) and (c) alone is always at least $|V|-1$ before accounting for cancellation. Thus this bound doesn't seem to be particularly useful without more work, though I may have missed something as it's late.
May 3, 2019 at 0:33 history answered Steven Landsburg CC BY-SA 4.0