Question

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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Answer 1

Answer:

This suggests that we color every point on the plane either white or black, making sure to use infinitely many of each color. With these constraints it is indeed the case that there must be a black point and a white point at unit distance. (In fact, "infinite" can be weakened to nonempty.)

Explanation:

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Answer 2

Answer:

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