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Topic: Discussion with WM - Frustration reaches boiling point (What
is not clear?)

Replies: 1   Last Post: Jul 8, 2014 6:09 AM

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Posts: 397
Registered: 8/11/06
Re: Discussion with WM - Frustration reaches boiling point (What
is not clear?)

Posted: Jul 8, 2014 6:09 AM
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Am 08.07.2014 11:57, schrieb
> On Tuesday, 8 July 2014 10:14:23 UTC+2, karl wrote:

>> The only thing you show is that a finite number of natural numbers is never
>> enough to enumerate all rationals; nobody doubts that.

> Sorry, all finite natural numbers are not enough. If there are infinitely many,
> why then should my proof for all not show it for all?

>> But for increasing n all rationals gets their index number.
> Not even in the limit, since in the limit the cardinality, i.e.,
>the number of not enumerated rationals is infinite.

This is your belief. in the enumeration given by Virgil

all rationals get their index here. Can you name any rational without an index?
No, therefore you prove nothing, you only claim that something which is vaild for all finite natural numbers MUST BE
TRUE also for something
infinite. This is not correct.

>> All rationals get their index here. But, certainly, always for a
>> given finite natural number there is an infinity of rationals which
>> have indices larger than this number n. But this shows nothing.

> A proof for all n shows nothing?

It shows only that a finite number of naturals is not enough to provide indices for all rationals. That's it!!

Don't be sad:

What is now with your proof that the reals are countable:

Why you don't say if it is right or wrong? I'm just curious.

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