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.

(if you answer this question I will give 100 point and mark as brainlest )​

Answer 1

In my opinion, for this if we just imagine the scenario we comes up with a picture with infinite white dots on black background" or vice versa . 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.

Answer 2

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.)