Re: Epistemology 201: The Science of Science

From: robert j. kolker (nowhere_at_nowhere.net)
Date: 02/08/05 

Date: Tue, 08 Feb 2005 17:22:50 -0500

Tony Orlow (aeo6) wrote:
> Bob, cmon! That's incorrect if that interval is contained as a proper
> subset of that euclidian space.

No. No. Google <Peano Curve>. This is a continuous 1-1 mapping of a
finite interval onto the interior of a square. The characteristic of an
infinite set is that there exists a proper subset of it such that the
-entire- set can be put into one one correspondence with the proper subset.

Infinite sets produce a lot of counterintuitive results. The solution:
give up your intuition based on finite sets. It is wrong.

Bob Kolker

Relevant Pages

  • Re: Epistemology 201: The Science of Science
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