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Topic: Proof 0.999... is not equal to one.
Replies: 194   Last Post: Feb 16, 2017 5:56 PM

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 William Hughes Posts: 4,277 Registered: 12/6/04
Re: Proof 0.999... is not equal to one.
Posted: Jun 1, 2007 4:50 PM

On Jun 1, 2:10 pm, chaja...@mail.com wrote:
> On Jun 1, 1:24 am, hagman <goo...@von-eitzen.de> wrote:

>
> > Take any element x of [0,1).
> > If x is the reciprocal of a natural number, map x to -x/(1-x).
> > Otherwise, map x to -x.

>
> > Which value will not pair?

<snip "proof" involving the undefined term
"infinite completion" that there must be an element that
does not pair>

If you beleive that your putative proof is correct you must
believe the conclusion:

there is an element that does not pair
and furthermore this element is the reciprocal of a
natural number.

You are now in the remarkable position of believing both

1. For every natural number N, the number 1/N
is part of a pair.

2. There is a reciprocal of a natural number that is
not part of a pair.

I hope you have been taking your Red Queen lessons.

- William Hughes

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