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: alternation implies 1-1 by SilverKnight)

Unfortunately no...

While the idea of alternation wasn't mine, it makes conceptual sense to me. Unfortunately the math in the case is not conceptual...

The reason that these explanations do not help my understanding is that they both work back to the comment I made regarding no smallest number, which I am clear on. But really this is a moot point, as I didn't believe it (the alteration of rationals and irrationals) to begin...

And darn you SK for bringing set theory into the game! :)

by the way, it appears that DJ missed a "not" in the last line of his post.

Posted by Cory Taylor on 2003-12-02 13:58:59