
Re: Infinity and all the rest
Posted:
Oct 24, 2013 10:09 AM


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 (n1, n]. Take off the rational >>> number > q_n (as enumerated by Cantor). Go > to step n+1.
>> Why should (n1,n] contain q_n?
> Use Cantor's enumeration. 1, 1/2, 2/1, 1/3, 3/1,... > The intervals (n1, n] are always ahead of the q_n contained within them.
Ok, you mean M_1 = empty set, M_{n+1} = (M_n u (n1, 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

