Newsgroups: sci.math
From: hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Date: Thu, 29 Oct 1992 21:15:12 GMT
Subject: Re: Infinite Problems

m...@cbnewsg.cb.att.com (marc.a.levy) writes:

> A road, infinte length, and 1 meter wide needs to be paved.
> The thickness of the pavement is given by h= e^-x
> This is to be done with 1 cubic meter of pavement.. How??

As infinite-length roads do not exist in our universe, it is clear
that your problem does not correspond to a real scenario.  But the
extent to which your scenario diverges from reality, and the manner of
its divergence, is not specified in the problem.  So the problem is
poorly posed, and we might as well suppose that we will decompose the
given stere into unmeasurable sets, and put it back together to form
two steres, as in the Banach-Tarski paradox.

In some dimensions, I have heard, Banach-Tarski does not allow us to
change the volume of our cement.  Well enough, then, we can break it
into uncountably many points of cement and biject them discontinuously
onto any road we care to pave.  Too easy.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil