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Topic: Only for mathematicians!
Replies: 26   Last Post: Aug 22, 2014 6:59 PM

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Ben Bacarisse

Posts: 1,404
Registered: 7/4/07
Re: Only for mathematicians!
Posted: Aug 18, 2014 4:30 PM
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mueckenh@rz.fh-augsburg.de writes:

> On Monday, 18 August 2014 20:46:40 UTC+2, Virgil wrote:
>

>> For example. WM's argument saying for every n the set of naturals up to
>> n does not ennumerate all of Q+, thus |N does not ennumerate Q+ or Q is
>> based on the clearly false assumption that what is true for every FISON
>> (Finite Initial Set Of Naturals up to some n in |N) must be true for the
>> infinite set of naturals, |N.

>
> For indexing are only finite natural numbers available. What cannot be
> indexed by them, cannot be indexed at all. Your mystical "set |N" is
> nothing more than all n - in mathematics.


An excellent example of fine words with no mathematical significance.
What are "available" numbers? Set theory has no such notion. And in
set theory, "indexed" means being put into bijection with N -- something
you've reluctantly agreed to for Q+. Un-indexed members of a set would
not be in the image of the bijection -- again, you've agreed that no
such positive rational exists. It's all just rhetoric based on, sadly,
deliberately misleading use of terms.

--
Ben.



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