Received: from mail-vw0-f61.google.com ([209.85.212.61])
	by chain.digitalkingdom.org with esmtp (Exim 4.72)
	(envelope-from <lojban-beginners+bncCML0xpmUARCX0cbkBBoEyZaxtQ@googlegroups.com>)
	id 1Ow6rs-0004vh-Qo; Wed, 15 Sep 2010 22:18:49 -0700
Received: by vws6 with SMTP id 6sf659420vws.16
        for <multiple recipients>; Wed, 15 Sep 2010 22:18:38 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
        d=googlegroups.com; s=beta;
        h=domainkey-signature:received:x-beenthere:received:received:received
         :received:received-spf:received:mime-version:received:received
         :in-reply-to:references:date:message-id:subject:from:to
         :x-original-sender:x-original-authentication-results:reply-to
         :precedence:mailing-list:list-id:list-post:list-help:list-archive
         :sender:list-subscribe:list-unsubscribe:content-type;
        bh=/lUu919VlJvwFu1aOT341zwugvvFbNez4HHCo/aPL/Q=;
        b=n3obSk87wAMp+vqegV05a0ELNyMckTxrzloO9q2+oXT73hp/Hqp3OdwmXVfd3BHW9a
         jtn/yC2zpjxSxCkXzIjGu1fme5qFxq2hKByvM/81C842smOWF+fYNQoR60W4Di0Ri8uT
         mKXPjZQL0mINsu0ov9wKVryv65QN0QR+oofUM=
DomainKey-Signature: a=rsa-sha1; c=nofws;
        d=googlegroups.com; s=beta;
        h=x-beenthere:received-spf:mime-version:in-reply-to:references:date
         :message-id:subject:from:to:x-original-sender
         :x-original-authentication-results:reply-to:precedence:mailing-list
         :list-id:list-post:list-help:list-archive:sender:list-subscribe
         :list-unsubscribe:content-type;
        b=USHtiphtfFVKNEHYE/KZQgtTZLjaMR7P8AIatymq0OlImUREcu7t33mwQ/fOYdQqXj
         ZKWTNzBMa7q9KMRFaurCOUWX5LySLIxcMMV7AbdzIeJdrUrIAQuJh7XuF7Hj4MUdX8xX
         hRAGJpQ/LD8pZYOASc+hmSPqFgidMYfINyINg=
Received: by 10.220.171.206 with SMTP id i14mr192727vcz.19.1284614295417;
        Wed, 15 Sep 2010 22:18:15 -0700 (PDT)
X-BeenThere: lojban-beginners@googlegroups.com
Received: by 10.220.111.137 with SMTP id s9ls473697vcp.1.p; Wed, 15 Sep 2010
 22:18:14 -0700 (PDT)
Received: by 10.220.201.205 with SMTP id fb13mr711140vcb.22.1284614294310;
        Wed, 15 Sep 2010 22:18:14 -0700 (PDT)
Received: by 10.220.201.205 with SMTP id fb13mr711139vcb.22.1284614294275;
        Wed, 15 Sep 2010 22:18:14 -0700 (PDT)
Received: from mail-qw0-f47.google.com (mail-qw0-f47.google.com [209.85.216.47])
        by gmr-mx.google.com with ESMTP id s4si288483vck.12.2010.09.15.22.18.13;
        Wed, 15 Sep 2010 22:18:13 -0700 (PDT)
Received-SPF: pass (google.com: domain of blindbravado@gmail.com designates 209.85.216.47 as permitted sender) client-ip=209.85.216.47;
Received: by qwa26 with SMTP id 26so421005qwa.20
        for <lojban-beginners@googlegroups.com>; Wed, 15 Sep 2010 22:18:13 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.224.37.14 with SMTP id v14mr1803355qad.298.1284614293022; Wed,
 15 Sep 2010 22:18:13 -0700 (PDT)
Received: by 10.229.101.208 with HTTP; Wed, 15 Sep 2010 22:18:12 -0700 (PDT)
In-Reply-To: <201009152248.22472.phma@phma.optus.nu>
References: <AANLkTinMiz+s_iOc6Wf_3hS971tiH0bE5+BtZLo6MZew@mail.gmail.com>
	<201009152248.22472.phma@phma.optus.nu>
Date: Thu, 16 Sep 2010 01:18:12 -0400
Message-ID: <AANLkTik5SaFEy78vbvHcinrFy+Dn+2AnenAYr-deaCz-@mail.gmail.com>
Subject: Re: [lojban-beginners] Cauchy sequences
From: Ian Johnson <blindbravado@gmail.com>
To: lojban-beginners@googlegroups.com
X-Original-Sender: blindbravado@gmail.com
X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com:
 domain of blindbravado@gmail.com designates 209.85.216.47 as permitted
 sender) smtp.mail=blindbravado@gmail.com; dkim=pass (test mode) header.i=@gmail.com
Reply-To: lojban-beginners@googlegroups.com
Precedence: list
Mailing-list: list lojban-beginners@googlegroups.com; contact lojban-beginners+owners@googlegroups.com
List-ID: <lojban-beginners.googlegroups.com>
List-Post: <http://groups.google.com/group/lojban-beginners/post?hl=en_US>, <mailto:lojban-beginners@googlegroups.com>
List-Help: <http://groups.google.com/support/?hl=en_US>, <mailto:lojban-beginners+help@googlegroups.com>
List-Archive: <http://groups.google.com/group/lojban-beginners?hl=en_US>
Sender: lojban-beginners@googlegroups.com
List-Subscribe: <http://groups.google.com/group/lojban-beginners/subscribe?hl=en_US>,
 <mailto:lojban-beginners+subscribe@googlegroups.com>
List-Unsubscribe: <http://groups.google.com/group/lojban-beginners/subscribe?hl=en_US>,
 <mailto:lojban-beginners+unsubscribe@googlegroups.com>
Content-Type: multipart/alternative; boundary=000e0cd341c29be86104905992df
Content-Length: 6769

--000e0cd341c29be86104905992df
Content-Type: text/plain; charset=ISO-8859-1

That makes sense, but should that really be the x2? Or should there be
another predicate that we use to relate numbers and sequences? For example,
we could say:
x1 is a Cauchy sequence converging to limit x2 in metric space x3.


mi'o bazu klama ti tu zi'o

On Wed, Sep 15, 2010 at 10:48 PM, Pierre Abbat <phma@phma.optus.nu> wrote:

> 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
>
> --
> You received this message because you are subscribed to the Google Groups
> "Lojban Beginners" group.
> To post to this group, send email to lojban-beginners@googlegroups.com.
> To unsubscribe from this group, send email to
> lojban-beginners+unsubscribe@googlegroups.com<lojban-beginners%2Bunsubscribe@googlegroups.com>
> .
> For more options, visit this group at
> http://groups.google.com/group/lojban-beginners?hl=en.
>
>

-- 
You received this message because you are subscribed to the Google Groups "Lojban Beginners" group.
To post to this group, send email to lojban-beginners@googlegroups.com.
To unsubscribe from this group, send email to lojban-beginners+unsubscribe@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/lojban-beginners?hl=en.


--000e0cd341c29be86104905992df
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

<div>That makes sense, but should that really be the x2? Or should there be=
 another predicate that we use to relate numbers and sequences? For example=
, we could say:</div><div>x1 is a Cauchy sequence converging to limit x2 in=
 metric space x3.=A0</div>
<div><br></div><div><br></div><div>mi&#39;o bazu klama ti tu zi&#39;o</div>=
<div><div><br><div class=3D"gmail_quote">On Wed, Sep 15, 2010 at 10:48 PM, =
Pierre Abbat <span dir=3D"ltr">&lt;<a href=3D"mailto:phma@phma.optus.nu">ph=
ma@phma.optus.nu</a>&gt;</span> wrote:<br>
<blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p=
x #ccc solid;padding-left:1ex;"><div class=3D"im">On Wednesday 15 September=
 2010 20:01:06 Ian Johnson wrote:<br>
&gt; I found myself being lazy in my analysis class having to repeatedly wr=
ite:<br>
&gt; Let x in R. Suppose {x_k} is a Cauchy sequence representing x.<br>
&gt; I was trying to come up with a good word to use to represent this clun=
ky<br>
&gt; relation, that is:<br>
&gt; x1 is a Cauchy sequence representing the real number x2.<br>
&gt; The thing I came up with first was pretty bad, but I didn&#39;t have a=
<br>
&gt; dictionary on me. It was {listrkoci}. Once I got to a dictionary I tho=
ught<br>
&gt; of {porsrkoci}, which seems a bit better. Does anyone have any better<=
br>
&gt; ideas? Maybe something that isn&#39;t a fu&#39;ivla?<br>
<br>
</div>&quot;porsrkoci&quot; and &quot;pornkoci&quot; are both good, and are=
 different forms of the same<br>
word (though the Book doesn&#39;t say that different rafsi of one gismu are=
<br>
equivalent, except in lujvo). The alternatives are a lujvo, which would be<=
br>
longish, and &quot;kocis.zei.porsi&quot;, which is also longish. I&#39;d go=
<br>
with &quot;pornkoci&quot;.<br>
<div class=3D"im"><br>
&gt; To clarify, this should hold, if broda is assigned to this relation:<b=
r>
&gt; li pa ce&#39;o li pa fi&#39;u re ce&#39;o li pa fi&#39;u ci ce&#39;o .=
.. broda li no<br>
&gt; (sorry that I don&#39;t know a good way to say &quot;et cetera ad infi=
nitum&quot; in<br>
&gt; lojban.)<br>
<br>
</div>I think the place structure should be &quot;x1 (sequence) is a Cauchy=
 sequence in<br>
x1 (metric space)&quot;. I know a sequence of rational numbers which conver=
ges to<br>
+3 in the real numbers and to -3 in the 2-adic numbers. There are Cauchy<br=
>
sequences of rational numbers which don&#39;t converge to any rational numb=
er,<br>
and there are sequences of rational numbers which are Cauchy sequences in o=
ne<br>
metric but not in another.<br>
<br>
Pierre<br>
--<br>
li fi&#39;u vu&#39;u fi&#39;u fi&#39;u du li pa<br>
<font color=3D"#888888"><br>
--<br>
You received this message because you are subscribed to the Google Groups &=
quot;Lojban Beginners&quot; group.<br>
To post to this group, send email to <a href=3D"mailto:lojban-beginners@goo=
glegroups.com">lojban-beginners@googlegroups.com</a>.<br>
To unsubscribe from this group, send email to <a href=3D"mailto:lojban-begi=
nners%2Bunsubscribe@googlegroups.com">lojban-beginners+unsubscribe@googlegr=
oups.com</a>.<br>
For more options, visit this group at <a href=3D"http://groups.google.com/g=
roup/lojban-beginners?hl=3Den" target=3D"_blank">http://groups.google.com/g=
roup/lojban-beginners?hl=3Den</a>.<br>
<br>
</font></blockquote></div><br></div></div>

<p></p>

-- <br />
You received this message because you are subscribed to the Google Groups "=
Lojban Beginners" group.<br />
To post to this group, send email to lojban-beginners@googlegroups.com.<br =
/>
To unsubscribe from this group, send email to lojban-beginners+unsubscribe@=
googlegroups.com.<br />

For more options, visit this group at http://groups.google.com/group/lojban=
-beginners?hl=3Den.<br />



--000e0cd341c29be86104905992df--