Re: Neighbors in Space
- From: mstemper@xxxxxxxxxxxxxxxxxxxx (Michael Stemper)
- Date: Fri, 1 May 2009 12:45:45 +0000 (UTC)
In article <75v1cqF1ae4fcU1@xxxxxxxxxxxxxxxxxx>, Robert Bannister <robban1@xxxxxxxxxxx> writes:
Ilmari Karonen wrote:
(In case you're curious, the five requirements usually made of a
metric are 1. that the distance between two points should be a
non-negative real number, 2. that the distance from a point to itself
should be zero, 3. that the distance from a point to any _other_ point
should not be zero, 4. that the distance from A to B should be the
same as the distance from B to A, and 5. that no path from A to B via
some other points should be shorter than their direct distance.)
Some interesting stuff. Point 2 puzzled me - I suppose I shouldn't ask
how it could be anything but zero in case the answer is even more puzzling.
Well, that's why the person or people who came up with the concept of
metric function included that requirement in the definition.
These properties are used to proved things about objects called "metric
functions". Then, any time that you find a function f:SxS->R that has
these properties, you know that all of the theorems that you've proved
about metric functions apply to it.
--
Michael F. Stemper
#include <Standard_Disclaimer>
Why doesn't anybody care about apathy?
.
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