The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Michael Klemm

Posts: 133
Registered: 11/13/12
Re: Infinity and all the rest
Posted: Oct 24, 2013 10:09 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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?


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.