[FOM] counted sets

[Lasse Rempe]

joeshipman at aol.com wrote:
> I suppose if there were a set of real numbers which was 
> not obviously countable from its definition, but for which there was a 
> nontrivial proof that its points were all isolated, one would have a 
> countable set that was not "counted". 
>   
It seems to me that would also not require choice, since we can write 
down an explicit injection of some countable basis of the topology of 
the real numbers (e.g. open intervals with rational endpoints) into N. 
This then leads to an injection of the given set into N.

Lasse

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Dr. Lasse Rempe
Dept. of Math. Sciences, Univ. of Liverpool, Liverpool L69 7ZL
Office 505; tel. +44 (0)151 794 4058, fax +44 (0)151 794 4061
http://pcwww.liv.ac.uk/~lrempe
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