Re: Epistemology 201: The Science of Science
From: Neil W Rickert (rickert+nn_at_cs.niu.edu)
Date: 03/07/05
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Date: Mon, 7 Mar 2005 18:56:17 +0000 (UTC)
Tony Orlow (aeo6) <aeo6@cornell.edu> writes:
>Thanks for the explanation. However, this doesm't seem different in a
>significant way from ordering the sets to achieve your mapping.
Any time you form a mapping between the integers and another set,
that will seem like ordering, simply because the integers have a
natural order.
[snip]
>Sure, you can use a mapping of A/B(i)=R(i)=i/1 and I(a/b)=2^a*3^b, but
>since this mapping is not symmetrical, it describes even less precisely
>the relationship between the sets.
We might say that there are two partial mappings. The proof of
Schroeder-Bernstein shows how to cut an paste parts of these mappings
to construct a complete mapping.
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