Re: abundance of irrationals
From: Dave Seaman (dseaman_at_no.such.host)
Date: 01/09/05
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Date: Sun, 9 Jan 2005 15:33:47 +0000 (UTC)
On 9 Jan 2005 06:11:23 -0800, mueckenh@rz.fh-augsburg.de wrote:
> Keith A. Lewis wrote:
>> I can set up a process to go through the natural numbers. It is true
> that
>> this process will never finish, but if you choose any particular
> natural
>> number I can tell you when it will be visited.
> If you believe, that this completes infinity (leading to aleph_0
> natural numbers) then you should admit that the same is true for the
> following construction of all reals, leading to aleph_0 binary digits
> (and more are not possible, even for transcendental numbers:
> 0.1
> 0.01, 0.11
> 0.001, 0.101, 0.011, 0.111
> ...
> Always insert 0 or 1 behind the point of each number given in the last
> line. You'll get them all.
At which position in this list does the rational number 1/3 appear?
-- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. <http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
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