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From: Pierre Abbat <phma@phma.optus.nu>
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Subject: Re: [lojban-beginners] Cauchy sequences
Date: Wed, 15 Sep 2010 22:48:20 -0400
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On Wednesday 15 September 2010 20:01:06 Ian Johnson wrote:
> I found myself being lazy in my analysis class having to repeatedly write:
> Let x in R. Suppose {x_k} is a Cauchy sequence representing x.
> I was trying to come up with a good word to use to represent this clunky
> relation, that is:
> x1 is a Cauchy sequence representing the real number x2.
> The thing I came up with first was pretty bad, but I didn't have a
> dictionary on me. It was {listrkoci}. Once I got to a dictionary I thought
> of {porsrkoci}, which seems a bit better. Does anyone have any better
> ideas? Maybe something that isn't a fu'ivla?

"porsrkoci" and "pornkoci" are both good, and are different forms of the same 
word (though the Book doesn't say that different rafsi of one gismu are 
equivalent, except in lujvo). The alternatives are a lujvo, which would be 
longish, and "kocis.zei.porsi", which is also longish. I'd go 
with "pornkoci".

> To clarify, this should hold, if broda is assigned to this relation:
> li pa ce'o li pa fi'u re ce'o li pa fi'u ci ce'o ... broda li no
> (sorry that I don't know a good way to say "et cetera ad infinitum" in
> lojban.)

I think the place structure should be "x1 (sequence) is a Cauchy sequence in 
x1 (metric space)". I know a sequence of rational numbers which converges to 
+3 in the real numbers and to -3 in the 2-adic numbers. There are Cauchy 
sequences of rational numbers which don't converge to any rational number, 
and there are sequences of rational numbers which are Cauchy sequences in one 
metric but not in another.

Pierre
-- 
li fi'u vu'u fi'u fi'u du li pa

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