You have an ink stamp that is so amazingly precise that, when inked and pressed down on the plane, it makes every circle whose radius is an irrational number (centered at the center of the stamp) black.

Is it possible to use the stamp three times and make every point in the plane black?

If it is possible, where would you center the three stamps?

(In reply to re(5): Brian's solution by Cory Taylor)

Countable means that you can establish a one to one correspondence with the integers and talk about first, second etc. It does not mean finite. Not only are the rationals countable but so are the algebraic (non transcendental) numbers. Countable sets have measure zero in set theory and the continuum is measure one.

Posted by Larry Settle on 2003-12-08 15:44:18