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.
