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.