Date: Wed, 19 Jun 1996 17:17:07 -0500 From: rahul-AT-peaches.ph.utexas.edu (Rahul Mahajan) Subject: Re: ..cat > The intuitiionist argument (see Brouwer) is that >just writing 1, 2, 3, ... or an 8 on its side is not a >complete description. These are labels, or indicators, >but not complete descriptions. In fact they argue that >finite mentalities cannot "fully describe" infinity by >any means. Of course intuitionism is a minority view >among mathematicians. >Barkley Rosser I didn't recognize the name earlier. Brouwer was the guy who rejected the axiom of the excluded middle and wanted to rebuild mathematics using only constructive proofs (funny, I don't think there's a constructive proof of his famous fixed-point theorem.). It always seemed totally bizarre to me. Fortunately, other mathematicians didn't agree, or we'd only have 10% of the mathematics that we actually have. Anyway, the definition of infinity is a lot further along than 1,2,3,... or an 8 on its side. The simplest definition I know is that an infinite set is one that is equipollent with at least one proper subset of itself (i.e., there exists a bijection between them). Describes infinity well enough for me, but then reductio ad absurdum was always good enough for me too. Rahul --- from list marxism2-AT-lists.village.virginia.edu ---
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