Article View: sci.physics
Article #3343Re: Possible?: 2 integers specifying a point in 3D space.
From: Joshua W. Burton
Date: Sat, 26 Sep 1992 05:02
Date: Sat, 26 Sep 1992 05:02
19 lines
1551 bytes
1551 bytes
I'm not quite sure where this one is leading, so I'm worried about tricks and traps, but I think everyone will agree with the following: The set of integers is countable; so is the set of n-tuples of integers, for all finite n. The set of real numbers is not countable; therefore we cannot label the real axis, much less any higher-dimensional Euclidean space, with two (or any finite number of) integers. If you think you have an integer- valued list of all the real 3-tuples, or even of all the real numbers on some open interval, please show it to me, and I will point out a real number that you forgot to list. It _is_, of course, possible to label all the points in 3-dimensional space with only two _real_ coordinates...but not in a way that preserves the notion of proximity. Hope this answers the question. -- Stadium sedipilae opt- |====================================================== imum Saeptum Paludosum | Joshua W. Burton burton@het.brown.edu (401)351-5908 etiamnunc est. Ain tu? |======================================================
Technical Details
Message-ID:
<1a0qsoINNkvv@stanley.cis.Brown.EDU>Path:
arc1-ca.pugleaf.net!sparky!uunet!wupost!sdd.hp.com!nigel.msen.com!yale.edu!qt.cs.utexas.edu!news.Brown.EDU!burtonReferences:
<Bv1rAG.LCw@cs.dal.ca>Show Full Headers
Complete Article Headers
Path: arc1-ca.pugleaf.net!sparky!uunet!wupost!sdd.hp.com!nigel.msen.com!yale.edu!qt.cs.utexas.edu!news.Brown.EDU!burton From: burton@cfm.brown.edu (Joshua W. Burton) Newsgroups: sci.physics Subject: Re: Possible?: 2 integers specifying a point in 3D space. Date: 26 Sep 1992 05:02:16 GMT Organization: Brown University Center for Fluid Mechanics Lines: 20 Message-ID: <1a0qsoINNkvv@stanley.cis.Brown.EDU> References: <Bv1rAG.LCw@cs.dal.ca> NNTP-Posting-Host: qcd2.het.brown.edu