Re: Extrapolating linear ratios

On 19 Dez., 12:35, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
On Thu, 18 Dec 2008 13:23:35 -0800 (PST), WM





<mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 18 Dez., 20:37, stevendaryl3...@xxxxxxxxx (Daryl McCullough) wrote:
WM says...

Assume you are dreaming. You have a nightmare. Is it possible to prove
by logic that you are dreaming? No. Some realms simply are
unaccessible to logic, in particular such that do not exist - like the
nightmare of completed infinity.

I think that you've got this analogy backwards. *You* are dreaming,

I think that the cardinal number of a set of positive even numbers
cannot surpass the values of all elements of the set.

An argument in favour of my position lies in the obeservation that
this is true for every finite set.

I on the other hand think that birds cannot fly. An argument in
favor of this is the fact that monkey's can't fly. Nor can cats or
dogs.

What's that? Birds are not monkeys you say? Hmm, never mind.

Infinite sets are not finite.

Not accepted argument. The infinite set of even numbers consists only
of finite even numbers. For every finit even number we can prove that
it consumes more than one interval of length 1. This property is
independent of the number of numbers considered.

You cannot prove that aleph_0 is a number. "There exists a set" is not
sufficient to conclude that that set has a cardinal number that is in
trichotomy with natural numbers.

Regards, WM
.

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