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