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(4): alternation implies 1-1 by Cory Taylor)

Hmmm...
"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."

What I had said was:
"The idea of alternation would imply equal numbers in the sense of 1-to-1 correspondence. But there are many more irrational numbers on the radius than rational. There are Aleph-1 of the former, but only Aleph-null of the latter. The numbers are intimately mixed, but not alternating."

I don't see that I accepted that the types alternate; rather I was stating what you state: it's the same as a 1-to-1 correspondence.

BTW, does anyone know of an HTML code for an Aleph?

Posted by Charlie on 2003-12-03 08:46:51