🚀 go-pugleaf

In article <Bv1rAG.LCw@cs.dal.ca> gauthier@ug.cs.dal.ca (Paul Gauthier) writes:
>From: gauthier@ug.cs.dal.ca (Paul Gauthier)
>Subject: Possible?: 2 integers specifying a point in 3D space.
>Date: 23 Sep 92 19:54:15 GMT

>I've been toying with something in my head for a while now and before I
>make an ass of myself by explaining it I'll first ask a related question:

>Is it possible to specify uniquely, an arbitrary point in 3D space using 
>only 2 integers? IE: You point to any point in space (using a conventional
>three-tuple (x, y, z)). Is it possible for me to respond with 2 integers
>which corrispond to that point and no other? You can even use real numbers
>in your three-tuple, but my response has to be two integers. Also, the
>3D space is infinite in all directions, so the values of each component
>of your three-tuple are completely unconstrained. Is it possible for me
>to use some co-ordinate system and label the point you give me uniquely
>with 2 integers?

>Any thoughts, proofs or loud guffaws?

>PG
>-- 
>  ===========================================================================
>                               Paul Gauthier
>  cyclist, rock climber, skydiver, computer scientist (...in order of danger)
>  Electronic: gauthier@ug.cs.dal.ca  Voice: (902)462-8217  Fax: (902)420-1074

Relation to Jon Gauthier?

If my understanding of mathematics is correct, the infinity of real numbers 
is "greater" than the infinity of integers.  Since inf(integer) * 
inf(integer) = inf(integer), your two integers cannot possibly represent even
a single point on a one-dimensional line.  (Think about it, you can 
represent only fractions, but not transcendentals).
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