Date: Feb 26, 2013 4:04 PM
Author: Brian M. Scott
Subject: Re: Problems with Infinity?

On Tue, 26 Feb 2013 17:54:19 GMT, Wayne Throop
<throopw@sheol.org> wrote in <news:1361901259@sheol.org> in
rec.arts.sf.written,sci.math:

[...]

>: A story such as "The 4-D Doodler," that speculates about
>: a fourth spacial dimension, one dimension beyond our
>: known world of three dimensions, seemed promising to me,
>: the dilettante, at first. Perhaps 4-dimensional space
>: uses an exotic infinity. Alas, as Wolfram notes, it's
>: the same old infinity. An infinity that's independent
>: of spacial dimensions.


> It's c, or aleph-1 maybe, or whatnot.

It's c, or 2^\omega.

> It is not the infinity of natural numbers; it's bigger.
> So there's at least two infinities, not the "same old
> infinity". Similarly, the cardinality of the set of paths
> in n>=2 d space (if I'm remembering a close enough
> description) is bigger still.


No, it's also 2^\omega, since by definition a path is
continuous.

[...]

Brian