POV-Ray : Newsgroups : povray.off-topic : Random wonderings 0x20c26764ae15b956c9a5eb7c1a237639 : Re: Random wonderings 0x20c26764ae15b956c9a5eb7c1a237639 Server Time
3 Sep 2024 11:25:55 EDT (-0400)
  Re: Random wonderings 0x20c26764ae15b956c9a5eb7c1a237639  
From: Darren New
Date: 8 Mar 2011 12:06:44
Message: <4d766224$1@news.povray.org>
Roman Reiner wrote:
> That depends on what numbers you are using. The number of points in the unit
> square of rational numbers is countable, the number of points in the unit square
> of irrational numbers is not.

Well, of course, yes. And the unit square of integers has a finite number of 
points in it. :-P

> By the way, IIRC, it is actually possible to constuct a bijection from [0,1]
> onto the unit square, meaning there is actually the same number of points in the
> unit square as there are points between 0 and 1.

Yep. There's really only two infinities you get when you talk about 
"numbers" - Aleph0 and Aleph1.

-- 
Darren New, San Diego CA, USA (PST)
  "How did he die?"   "He got shot in the hand."
     "That was fatal?"
          "He was holding a live grenade at the time."


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