There are infinite black and white dots on a plane. Prove that the distance between one black dot and one white dot is one unit.
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We can't, because it's false. If all black dots happen to be on the line x=0and white dots on the line x=π (and the rest of the plane is neither white nor black), there is no such pair. ... The Questions and Answers of There are infinite black and white dots on a plane
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