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Topic: Infinity and all the rest
Replies: 15   Last Post: Oct 24, 2013 8:56 PM

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Registered: 1/29/05
Re: Infinity and all the rest
Posted: Oct 24, 2013 9:31 AM
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On Thursday, 24 October 2013 14:20:42 UTC+2, Michael Klemm wrote:
> WM wrote:
>> Start with n = 1 and the empty set M. In the nth step union M with the set > of all rationals of the interval (n-1, n]. Take off the rational number > q_n (as enumerated by Cantor). Go > to step n+1.

> Why should (n-1,n] contain q_n?

Use Cantor's enumeration. 1, 1/2, 2/1, 1/3, 3/1,...

The intervals (n-1, n] are always ahead of the q_n contained within them.

Regards, WM

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