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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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:
The statement is in general false: for example, if the black dots are all and only on the locus x=0, while the white ones are all and only on the locus x=2, then the assertion is false (we are using the Euclidean distance).