**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Sun, 4 Apr 1999 19:54:53 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 148] Re: [time 121] RE: [time 115] On Pratt's Duality [time 81]Entropy, wholeness, dialogue, algebras"**Previous message:**Ben Goertzel: "[time 146] Re: [time 114] Re: Pratt and Consciousness"**In reply to:**Stephen P. King: "[time 125] Re: [time 114] Re: Pratt and Consciousness"**Next in thread:**Ben Goertzel: "[time 150] Re: [time 81] Discreteness and p-adics"

On Sun, 4 Apr 1999, Ben Goertzel wrote:

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

p-adic norm also. For instance 1/1-p =1+p+p^2+.... is completely well

defined p-adic number with p-adic norm one.

One could argue that discreteness is only apparent but the fact p-adic

Fourier basis obeys Kronecker delta normalization suggests that this is

not the case.

MP

**Next message:**Stephen P. King: "[time 148] Re: [time 121] RE: [time 115] On Pratt's Duality [time 81]Entropy, wholeness, dialogue, algebras"**Previous message:**Ben Goertzel: "[time 146] Re: [time 114] Re: Pratt and Consciousness"**In reply to:**Stephen P. King: "[time 125] Re: [time 114] Re: Pratt and Consciousness"**Next in thread:**Ben Goertzel: "[time 150] Re: [time 81] Discreteness and p-adics"

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