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Re: Infinity and all the rest
Posted:
Oct 24, 2013 4:23 PM
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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
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