OASIS Mailing List ArchivesView the OASIS mailing list archive below
or browse/search using MarkMail.


Help: OASIS Mailing Lists Help | MarkMail Help

[Date Prev] | [Thread Prev] | [Thread Next] | [Date Next] -- [Date Index] | [Thread Index]
Re: [xml-dev] Infinity

On Sat, Mar 3, 2018 at 7:33 AM Norman Gray <norman@astro.gla.ac.uk>

It will be, but since there are as many elements in that set as there
are positive integers (they can be put into a one-to-one
correspondence), it is no bigger or smaller an infinity than the number
of integers.  In contrast, the number of real numbers is a 'larger
infinity' than the number of integers.  If you wish to further explore
this rabbit hole, see <https://en.wikipedia.org/wiki/Aleph_number> and
work outwards...

Actually no, and thankfully the Wikipedia page gets this right. Integers and reals are both of cardinality Aleph naught. The easiest way to conceptualize this equivalence is to think of them both as being mappable to a set of points on a line.  The set of solutions to all polynomials is traditionally considered not to be of Aleph naught, (one can think of this as being some what multidimensional). However, I have recently seen some arguments to the contrary, though I have not spent the time to dig into them.

Peter Hunsberger


Peter Hunsberger

[Date Prev] | [Thread Prev] | [Thread Next] | [Date Next] -- [Date Index] | [Thread Index]

News | XML in Industry | Calendar | XML Registry
Marketplace | Resources | MyXML.org | Sponsors | Privacy Statement

Copyright 1993-2007 XML.org. This site is hosted by OASIS