You don't, because it's false. If all black dots happen to be on the line y=0 and white dots on the line y=π (and the rest of the plane is neither white nor black), there is no such pair.
There are infinite black and white dots on a plane. ... 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.
Answers & Comments
You don't, because it's false. If all black dots happen to be on the line y=0 and white dots on the line y=π (and the rest of the plane is neither white nor black), there is no such pair.
Answer:
There are infinite black and white dots on a plane. ... 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.