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> inrec.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 iscontinuous.[...]Brian