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(3): alternation implies 1-1 by SilverKnight)
Well, it wasn't helpful because I already agree with all of your points, not because it didn't make sense. I never agreed that points could be adjacent to each other, I was simply replying to Charlies comment insofar as he could accept that the points could alternate, but not that they were 1-1. To me this was the same issue.
And in DJ's post, his final comment is meant to rebut the earlier claim that a single stamp will mark the entire plane. In fact he even disproves this very comment as part of his post. I have reposted his final remark, with the not I believe he intended included.
In any case, the answer is ~not~ that a single stamp will cover an entire plane.
re(4): alternation implies 1-1
