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
by Brian Wainscott)
Brian,
You wrote:
"...Larry was correct in his assertion that picking three points at random from the plane, the odds of covering all the points int the plane is 1. "
Examples of three distinct points have already been shown that do not cover the plane. Those three points are POSSIBLE to be chosen at random.
The fact that even one set (of three distinct points that having stamps centered on them) exists, that will not cover the plane, is sufficent to say you can't take any three points at random.
___________________________
As for your proof:
The conclusion may be correct, but the proof is lacking... you wrote:
"Any point D chosen from the complement of S(A,B) will give you three points (A,B,D) where you can stamp and cover the plane."
That is an assertion and you have not (yet) justified, explained, or otherwise proven it.
re:
