Re: Cantor's diagonal proof wrong?
stephen_at_nomail.com
Date: 11/16/04
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Date: 16 Nov 2004 17:42:55 GMT
Han de Bruijn <Han.deBruijn@dto.tudelft.nl> wrote:
: I have always learned that a mathematical proof should be CONVINCING in
: the first place. Obviously, Cantor's arguments are not convincing enough
: to prevent these heated discussions to be launched every time again. And
: what's worse, these counter arguments are continuing now for more than A
: WHOLE CENTURY. Thus it is highly unlikely that they will be stopped in
: the foreseeable future.
The proof is convincing to those who understand the ideas and
definitions used by the proof. A common theme among the people
who argue with the proof is that they do not really understand
the basic ideas used in the proof. For example, in this thread
the original poster did not know what an integer was. It is
not surprising that he does understand the proof when he does not
know what an integer is, and it is not surprising that he is not
convinced by something he understands. Many other people who
argue with the proof do not know what a real number is, or what
a function is, or what a set is, or what infinite means. The often think
they know what a real number or a function is, but it is often some
imprecise personal definition.
Cantor's proof draws a lot of attention for the same reason
that Relativity does. It is fairly simple conceptually,
it is counter to "common sense", and it relies on precise
definitions.
Stephen
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