Re: Infinity can not exist
From: David P. Ferguson (david.ferguson1_at_cox.net)
Date: 07/03/04
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Date: 3 Jul 2004 10:27:01 -0700
Michael II <MichaelII@spamshaft.net> wrote in message news:<WLmFc.14908$%_6.5586@attbi_s01>...
> Japcuh wrote:
> > It is impossible for infinity to exist, because in order for infinity
> > to exist, everything possible must happen. Including infinity not
> > existing. Therefore, it is possible for something to be an extrememly
> > large, but not infinite. For it to be infinite, it would have to be
> > finite at the same time.
> >
> > Japcuh
> > (Just Another Perl C Unix Hacker)
> > http://www.catb.org/~esr/faqs/hacker-howto.htm#what_is
> > .O.
> > ..O
> > OOO
>
> This thread is kinda beginning to resemble the ancient question: How
> many angels can dance on the head of a pin?
>
> Answer: All of them.
>
> Infinity may or may not exist depending on how the question is framed
> and in what context. There's a related concept from the Buddhist
> tradition of totality. Totality encompasses everything that is and by
> extension everything that isn't. That which totality isn't, defines all
> that totality is.
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DAVID FERGUSON SAYS:
If you ask whether 1=>2=>3=>etc..produces an infinite quantity.
That is: Can it be considered as an object of existence? (That is one
of the central problems isn't it?)Then I think you can say that
infinity exists. You are probobly thinking of something else so let me
say:
I think that the problem is not so much as whether infinity
exists in a worthwhile sense as is the problem of the nature of
infinity, once you allow its eXistence. The problem that I have with
the predominant views of the mathematical nature of infinity has to do
with the "insane" notion that infinite sets can be characterised as
having the same cardinalty as many of their proper subsets. If that is
true then infinite sets have a very tenuous hold on existence.
I am looking forward to a time when infinite sets are given a
basis which would require sets a and B to have the same size in order
for them to have the same cardinality. An example of the
inadequacy of current set cardinality "theory" Is: Card ("Evens") =
Card ("Naturals") even though the set of even natural numbers is a
proper subset of the set of Natural numbers. There is an obvious and
provable two to one correspondence between the Natural numbers and the
set of Even Natural numbers.(Two Naturals for every Even0 Yet the
cantorians INVENT a one to one correspondence between the two sets by
observing that there is a set of even numbers E*={m|m=nx2 for n an elt
of N} They then claim that the set E* is the set E={n|n even elt of
N}. It is clear that: Since
(1) Card(E)=Card(N)/2 and
(2) Card(E*) =Card(N)
E and E* cannot be the same set!!
I want infinite sets to have a basis which would prevent this kind of
insanity. GIVE ME AN INFINITE SET I CAN LIVE WITH.
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