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

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Infinity and all the rest
Posted: Oct 24, 2013 4:23 PM

On Thursday, 24 October 2013 21:49:21 UTC+2, Virgil wrote:

>> It is curious that so many mathematicians believe that this sequence of sets
>> could converge to the empty set.

> I do not know of any mathematicians who claim that.

Recognize yourself.

If the set M does never become empty, then never all rationals are enumerated.

> I challenge WM to show that there is even one rational that is not in the following well-ordering of the rationals

I can refer to such natural numbers only which belong to a FISON. It is well known that every for every FISON we have
|FISON|/ ||N| = 0.
So what would it help to show that I cannot show a rational that is not in your well-ordering?

> Consider this well-ordering of the rationals:

This is a well-ordering of a tiny subset of the rationals. You should know that up to every n, {1, 2, 3, ..., n} is in fact a fraction of zero measure compared to |N. So you must fail.

> Then the set of all rationals
Can you tell me how many naturals you need to well-order the first 1 % of all rationals?
Regards, WM

Date Subject Author
10/24/13 Virgil
10/24/13 mueckenh@rz.fh-augsburg.de
10/24/13 Michael Klemm
10/24/13 mueckenh@rz.fh-augsburg.de
10/24/13 Michael Klemm
10/24/13 mueckenh@rz.fh-augsburg.de
10/24/13 Virgil
10/24/13 mueckenh@rz.fh-augsburg.de
10/24/13 Brian Q. Hutchings
10/24/13 Virgil
10/24/13 mueckenh@rz.fh-augsburg.de
10/24/13 Virgil
10/24/13 Virgil
10/24/13 Virgil