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: by DJ)
I'm tired, DJ, but I just have to say a few quick words before I retire...
My final answer I think said the same thing as yours.
I was wrong in my proof, but I'm glad to see I got the right answer... As far as the point (0, 3) not being inked... My point was that a point means nothing as it's only used a means of reference and *doesn't* have depth... it's only when we think of actual areas and segments, that we can make claims to actual areas inked. I mean what does it really mean that the point (0, 3) will not be inked by the stamp?... Oh, wait--now I get it... this is a special idealized stamp and the paper is a special idealized plane where we're trying to cover even the rational points that one stamp cannot hit.
Well--shoot--that really makes it much harder, then.
re(2):
