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

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Michael Klemm

Posts: 95
Registered: 11/13/12
Re: Infinity and all the rest
Posted: Oct 24, 2013 10:09 AM
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WM wrote:
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.


Ok, you mean
M_1 = empty set, M_{n+1} = (M_n u (n-1, n]) - {q_n}.
But why is a recursive definition of sets M_n a super task?
What is curious in repect of this quite common method?

Regards
Michael





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