[FOM] Question on Number Line
Lawrence Stout
lstout at iwu.edu
Thu Nov 17 16:00:44 EST 2005
Suppose we take a different tack and claim that a physical string does
not correspond to a closed interval [a,b] in the reals, but rather to
an interval in which each interior point has a twin: if $a < c < b$
then there is another point $c'$ which is in exactly the same open sets
as $c$ and has exactly the same strict order relationships. Only the
endpoints remain untwinned. Note that from the topology and the order
we cannot distinguish $c$ and $c'$. When you cut such a string at $c$
you put $c$ in one half and $c'$ in the other. Since you cannot tell
them apart it does not matter which half gets which. The resulting cut
strings are homeomorphic to the original string and to eachother.
Lawrence Neff Stout
Professor of Mathematics
Illinois Wesleyan University
Bloomington, IL 61702-2900
http://www.iwu.edu/~lstout
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