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

Ben Goertzel (ben@goertzel.org)
Sun, 04 Apr 1999 12:21:11 -0400

>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!!!



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