Re: Zenkin's paper on Cantor (reply of Dr. Zenkin)
From: Han de Bruijn (Han.deBruijn_at_DTO.TUDelft.NL)
Date: 11/25/04
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Date: Thu, 25 Nov 2004 09:28:53 +0100
Jesse F. Hughes wrote:
> Cardinality is well-motivated to capture the size of a set. When a
> child counts a collection of pencils, he is creating a bijection
> between an initial segment of N and the set of pencils. For finite
> sets, assigning a size clearly involves a bijection.
>
> I've seen no reason why this isn't the essence of counting.
Except for a couple of nasty details. When "creating" the bijection,
the pencils must be labeled. Otherwise you wouldn't know if a pencil
has already be counted or not. Labeling the pencils actually means that
you are creating a different set: that of the pencils already counted.
Moreover, you are destroying the original set: that of the pencils still
to be counted. The process stops when the latter set has become empty.
Replacing the pencils by apples:
http://hdebruijn.soo.dto.tudelft.nl/fototjes/appels.htm
Han de Bruijn
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