A painter went to a single mathematical plane, and colored every single point on that plane one of two colors.

Prove that there exist two points on the plane that are exactly one meter apart and have the same color.

(In reply to by Monica)

You are mistaken..a plane is not another word for a line. A plane is an infinite 2-dimensional region, like a piece of paper that never ends, while line only has one dimension, stertching infinitely in either direction.

What you described is a line segment, part of a line with two definite endpoints, and an infinite number of points between them, since between any two points another point can be placed.

Posted by DJ on 2003-08-19 18:50:00