On Wed, 27 Nov 2002, Ken Hirsch wrote:
> Jim Choate writes:
> >
> > It's not I who is doing the misreading. I sent this along because I don't
> > know -your- level, which considering your understanding of
> > 'completeness'...
>
> Peter Fairbrother has said nothing inaccurate about completeness, whereas
> your statements about completeness having to do with the ability to write
> statements is nonsense.
Not hardly...but apparently Peter isn't the only one who doesn't quite
grasp 'complete'...
"A formalism is complete, if for every formula which - in accordance with
it's intended interpretation - is provable within the formalism, embodies
a true proposition, and if, conversely, every true proposition is embodied
in a provable formula."
The Philosophy of Mathematics
An introductory Essay
S. Korner
ISBN 0-486-25048-2 (Dover)
pp 77
And we can of course compare this to Cauchy Completeness...
Definition 6.4
Let X be a metric space, {x_n} a sequence of elements in X. Denote the
distance function by d. The sequence {x_n} is called a Cauchy sequence,
if given e>0, there is a positive integer N, so that whenever n and m are
greater than N,
d(x_n, x_m) < e
Definition 6.5
A metric space X is complete if every Cauchy sequence {x_n} in X converges
to an element in X (see Theorem 5.1).
Topology - An introduction to the point-set and algebraic areas
D.W. Kahn
ISBN 0-486-68609-4 (Dover)
pp 101
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