Re: limitation to induction on finite bounds

From: The Ghost In The Machine (ewill_at_aurigae.athghost7038suus.net)
Date: 07/03/04 

Date: Sat, 03 Jul 2004 16:00:09 GMT

In sci.logic, |-|erc
<gotcha@beauty.com>
 wrote
on Sat, 03 Jul 2004 02:36:44 GMT
<0ZoFc.76072$sj4.49693@news-server.bigpond.net.au>:
> "The Ghost In The Machine" <ewill@aurigae.athghost7038suus.net> wrote
>> >> >> >> The plot of the set of {0.3, 0.33, 0.333, ...} will cover 1/3, if
>> >>one uses your
>> >> >> >> procedure to draw all real numbers such that 03033 SetMinus r = 0.
>>
>> Depends on your definition of "cover". But OK, congratulations.
>> You've now proved that all sets are closed. (This is because
>> all sets cover their limit points, according to your definition-set.)
>>
>
> fine, so your set 010203 covers all reals from 0 to 1.
> cover meaning: Ar 0<r<1, T setminus r=0,
> not necessarily a bijection.

That it does. Of course it does not *include* all reals,
merely covers them -- if the definition of "cover"
includes SetMinus or its equivalent.

>
> Herc
> 

-- 
#191, ewill3@earthlink.net
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