Re: the Reals really have negative curvature built-in and negative-Reals are superfluous
- From: rem642b@xxxxxxxxx (Robert Maas, see http://tinyurl.com/uh3t)
- Date: Fri, 17 Jun 2005 13:15:52 -0700
> From: a_plutonium@xxxxxxxxxxx
> But it is terribly difficult to see that Reals are negative curvature
> of Lobachevskian geometry.
It's my understanding that the definition of "curvature" as applied to
a metric space, which distinguish Euclidean (flat) spaces from
hyperbolic etc. spaces, applies only to 2-dimensional spaces and by
extension to multi-dimensional. It doesn't apply to 1-dimensional
spaces, so what you say there seems to be meaningless. If you have a
meaning to the word "curvature" which applies to 1-dimensional spaces
such as the reals, please tell us that definition or post a link to an
online definition.
.
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