Re: Epistemology 201: The Science of Science

From: Albert (albertwagner_at_cox.net)
Date: 02/11/05 

Date: Fri, 11 Feb 2005 11:07:19 -0600

Tony Orlow (aeo6) wrote:
> stephen@nomail.com said:
>
>>In sci.math Tony Orlow (aeo6) <aeo6@cornell.edu> wrote:
>>: Or, you can simply admit that there are more real numbers between 0 and
>>: 2 than there are between 0 and 1, even if the "cardinality" is the same,
>>: for instance, 1.5.
>>: --
>>: Smiles,
>>
>>: Tony
>>
>>Whoever said that there were not numbers in [0,2] that were not in [0,1]?
>>What is true is that every element in [0,1] can be uniquely mapped to
>>an element in [0,2]. Why won't you simply admit that? :)
>>
>>Stephen
>>
>
> I never denied that. Cantor's cardinality is significant, and
> distinguishes between classes of infinity. I am making a valid point
> that there are details of infinity that it does not capture. There is a
> problem when idiots say there are the same number of reals between 0 and
> 1 as between 0 and 2, when one obvious has more reals than the other as
> a proper superset, just because there is the same Cantorian cardinality.
> Why can't you simply admit that?

Can a valid bijection be invented between the set of reals
between 0 and 1 and the set of reals between 0 and 2? It doesn't
seem so to me, in that all reals between 1 and 2 will be left
unmatched. But, hell, what do I know?

<snip> 

-- 
"Don't you see that the whole aim of Newspeak is to narrow the 
range of thought? In the end we shall make thoughtcrime literally 
impossible, because there will be no words in which to express it."
     -- George Orwell as Syme in "1984"

Relevant Pages

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