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Topic: Matheology 400: Quantifier Confusion
Replies: 12   Last Post: Dec 22, 2013 7:32 PM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Matheology 400: Quantifier Confusion
Posted: Dec 19, 2013 4:52 PM
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In article <de4e53cc-3403-4e80-9a4a-7671a71157c5@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:

> On Thursday, 19 December 2013 17:16:29 UTC+1, wpih...@gmail.com wrote:
>

> > However, note that when we use a indirect proof we use one and only one
> >
> > rational approximation to d.
> >

> Your proof holds for every fraction represented by every sum of d_n/10^n.
> Note however, the "infinite sum" is not a sum (that is only a sloppy kind of
> speech) but it is the limit of a sequence (of partial sums). Every partial
> sum has a decimal expansion. The limit has not (because all finite natural
> numbers n have been used up already and other natural numbers are not
> available).


The point is that every rational has a decimal expanson accurate to any
finite number of decimal places.

So in any list of rationals , the nth rational can be correctly known at
its nth decimal place and d may be made to differ from it at that place.

Thus the construction which proves WM wrong is right!
--





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