Question

There are infinite black and white dots on a plane. Prove that the distance between one black dot and white dot is one unit. ​

Answer 1

Answer:

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Explanation:

In either case we can see that plane is colored with black or white color only. So we can say that for each white dot there is exist a black dot at unit distance because if not than we end up coloring the full plane with white color.

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Answer 2

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

The statement is in general false: for example, if the black dots are all and only on the locus x=0x=0, while the white ones are all and only on the locus x=2x=2, then the assertion is false (we are using the Euclidean distance).Probably there are some more hypothesis in the background OR the aim of the question is just to analyze the way the candidate faces a given mathematical problem, reaching conclusions which can be in contrast with the thesis of any given question. .......... I hope so it will help you