[time 143] Re: [time 140] Re: [time 81] Discreteness and p-adics

Stephen P. King (stephenk1@home.com)
Sun, 04 Apr 1999 12:38:49 -0400

Hi guys,

        Are they not set-wise complements of each other? Like an independent
graph and a complete graph?



Ben Goertzel wrote:
> >p-Adic numbers with norm bounded by some upper bound
> >are of from x= p^rk , where k is possibly *infinite* integer
> >having pinary expansion k= SUM(n>=0) k_np^n. These numbers form a
> >discrete set! The real counterparts of these numbers in canonical
> >identification SUM x_np^n --> SUM x_np^(-n) however form a continuum!
> I don't understand this. It sounds like you are saying that a discrete set
> (cardinality aleph null) is isomorphic to a continuum (cardinality aleph one),
> which is impossible, and so obviously is not what you're really saying!!!
> ??
> ben

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