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Is the phrase "C is the set of points closer to A than to B" correct? Or must I write "C is the set of points which are closer to A than to B" ?

The last formulation seems a bit heavy to me and I'm looking for an alternative formulation. If you have some suggestions I would be most grateful.

  • I agree with @jasper that both sentences are correct and that explicitly writing out "which are" is more formal than omitting it. – ColleenV Jan 8 '15 at 22:04
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    Both can be correct, but in more formal English (at least sometime) it would be more common to use "that" instead of "which" since the clause is restrictive (instead of supplementary information) – eques Jan 8 '15 at 22:30
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Both options are correct. I agree with the original poster that the first option is simpler. The second option is more formal, and some mathematicians might prefer it.

Here are some shapes that can be described this way:

  • A half-plane (in 2-space, if A and B are symmetrical objects that do not overlap, such as points, lines, or circles)
  • The "interior" of a parabola (in 2-space, if A is a point and B is a line)
  • The "exterior" of a parabola (in 2-space, if A is a line and B is a point)
  • The "interior" of a paraboloid (in 3-space, if A is a point and B is a plane)
  • The "exterior" of a paraboloid (in 3-space, if A is a plane and B is a point)
  • Thanks ! Indeed this comes from a math research article I'm writing. Math papers can easily have heavy wording, but they can also have grammar mistakes. I'm trying to avoid both... – GeoffFirmin Jan 8 '15 at 22:26

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