Re: Cantor
- From: francisstephens@xxxxxxxxx
- Date: 15 Oct 2005 16:31:17 -0700
You have missed something. But a quick read of internet sources about
Cantor's argument shows that you've missed the same thing a alot of
other people. I think we need to clarify some subtleties.
You need to create a distinction between:
complete infinities
- Cantor's complete infinite set of the reals
potential infinity
- This is what you are talking about when you say that we have a
list of numbers that
can be of any length
Cantor was not talking about "any list of you can produce" we was
talking about "*the* complete list of reals"
These two lists have quite different properties. Cantor had to
postulate a complete list of the reals in order to show that this lead
to a contradiction.
Otherwise if allowed ourselves to use the "list of any length" approach
then we can very quickly show that for any list of integers we can
produce an integer not on that list. But this argument is clearly
unhelpful.
Have a look around at the arguments surround potential and actual
infinities, the concerns and difficulties are far from simple.
.
- References:
- Cantor
- From: Pedro
- Cantor
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