Re: Easy Question About p-adics

In article <281120051311347905%edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
G. A. Edgar <edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
>In article <dmfcdi$1jmj$1@xxxxxxxxxxxxxxxxxx>, Arturo Magidin
><magidin@xxxxxxxxxxxxxxxxx> wrote:

>> Take the sequence
>>
>> 1, 1+p, 1+p+p^2, 1+p+p^2+p^3, ...., 1+p+p^2+...+p^n, ...
>>
>> The sequence is Cauchy, since a_n = a_{n+k} (mod p^n) for all n,k>0,
>> so ||a_n - a_{n+k}|| = p^{-n}.
>>
>> The sequence does not converge to any rational.
>
>It converges to 1/(1-p) .

Does it? Man, I'm just on fire this morning. Did my other example fail
as well, or did I get that one right? (take the smallest positive
solution to solutions to x^2 = -1 (mod 5^n) as the n-th term).

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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