Re: A Guide for Cantor Cranks

Article View: sci.logic

Article #815

#815

From: William Hughes
Date: Thu, 24 Mar 2011 11:18

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On Mar 24, 7:12 am, Albrecht <albst...@gmx.de> wrote:
> On 24 Mrz., 10:31, William Hughes <wpihug...@gmail.com> wrote:
>
>
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> > Recall
> >  The anti-diagonal is formed by taking the
> >  diagonal and changing every 0 to 1 and 1 to 0.
> > Any claim that the anti-diagonal does not exist is
> > silly.  Any claim that the anti-diagonal is equal to
> > a row of the list is silly.
> > On Mar 24, 4:51 am, Albrecht <albst...@gmx.de> wrote:
>
> > <snip>
>
> > > Any claim that an irrational decimal number exists is silly.
>
> > > Pi has to be the limit of the serie
>
> > > 3/1, 31/10, 314/100, 3141/1000, 31415/10000, ...
>
> > > If you claim the existence of an irrational decimal number you claim
> > > the existence of the number
>
> > > 31415.../10000...
>
> > > with infinite numerator and inifite denominator.
>
> > Absolute piffle.  There is no reason that defining the
> > existence of the limit of finite ratios means that you
> > have to define either infinite quantities, or the ratio
> > of infinite quantities.
>
> So you admit that an infinite decimal number has crucial other
> properties than a finite decimal number?
>You admit that a number like
> 3.1415... is crucial different from a number like 0.75?

Nope. I said nothing about the differences between
an irrational number and a rational number.

> But you insist that the "behaviour" of a number like 3.1415... should
> be like the "behaviour" of a number like 0.75?

I said nothing of the sort.

My point is that while you need infinite sequences
of *finite* rations to
definite irrational numbers, you don't need either
infinite quantities or the ratio of infinite quantities.

                 - William Hughes

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From: William Hughes <wpihughes@gmail.com>
Newsgroups: sci.logic,sci.math,comp.theory,sci.physics,aus.science
Subject: Re: A Guide for Cantor Cranks
Date: Thu, 24 Mar 2011 04:18:17 -0700 (PDT)
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