From lojban+bncCOib25n_BhC2vLntBBoETtKh2w@googlegroups.com Tue Apr 19 21:17:10 2011 Received: from mail-qw0-f61.google.com ([209.85.216.61]) by chain.digitalkingdom.org with esmtp (Exim 4.72) (envelope-from ) id 1QCOqg-0002xj-GA; Tue, 19 Apr 2011 21:17:10 -0700 Received: by qwh5 with SMTP id 5sf470640qwh.16 for ; Tue, 19 Apr 2011 21:17:00 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=beta; h=domainkey-signature: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:x-google-group-id:list-post :list-help:list-archive:sender:list-subscribe:list-unsubscribe :content-type; bh=VPhACfcz1Yg/OcZ7ef8VVcgXZ4D568QVKPLpMAZu4FA=; b=boiErRXVw+LMHocSq3fIJLrE2cTwLhDHAw70l/x8uF/mnA4eCUSaKkrT9JQhqwIh3j 1lLqHVlxOJjXsEQia+DHOQW2bmBPEm3JtUYqj/pCGrLNtOQj20ZFa/BzamiyGjNJ3X30 RRbagu7i9MxkjN4RsW8+iXYlSUVPzIkrava0A= 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:x-google-group-id:list-post:list-help:list-archive:sender :list-subscribe:list-unsubscribe:content-type; b=g+Sr7tdy8lQEh8F6fnCXYMXp6I+nXBMpAczHsFcxT2jbCTlc+wwM/I8jYaR98rVBP1 fxJ0dm1YryX95Kg+b3JUMmxNlqxx3ZP9+jsjp8qFEDdjVl46iEjTY3IYOPgGV4USV3MZ dnMqHMtcrDa1heOC06Am2acUUWK/LbsH+dQXk= Received: by 10.224.198.199 with SMTP id ep7mr583356qab.59.1303273014417; Tue, 19 Apr 2011 21:16:54 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.229.220.212 with SMTP id hz20ls352181qcb.3.gmail; Tue, 19 Apr 2011 21:16:52 -0700 (PDT) Received: by 10.229.73.96 with SMTP id p32mr494780qcj.19.1303273012661; Tue, 19 Apr 2011 21:16:52 -0700 (PDT) Received: by 10.229.73.96 with SMTP id p32mr494779qcj.19.1303273012631; Tue, 19 Apr 2011 21:16:52 -0700 (PDT) Received: from mail-qy0-f176.google.com (mail-qy0-f176.google.com [209.85.216.176]) by gmr-mx.google.com with ESMTPS id f1si108225qcq.6.2011.04.19.21.16.52 (version=TLSv1/SSLv3 cipher=OTHER); Tue, 19 Apr 2011 21:16:52 -0700 (PDT) Received-SPF: pass (google.com: domain of rpglover64@gmail.com designates 209.85.216.176 as permitted sender) client-ip=209.85.216.176; Received: by mail-qy0-f176.google.com with SMTP id 30so217406qyk.7 for ; Tue, 19 Apr 2011 21:16:52 -0700 (PDT) MIME-Version: 1.0 Received: by 10.224.187.73 with SMTP id cv9mr4157849qab.26.1303273012327; Tue, 19 Apr 2011 21:16:52 -0700 (PDT) Received: by 10.224.28.203 with HTTP; Tue, 19 Apr 2011 21:16:52 -0700 (PDT) In-Reply-To: References: <201104182202.57948.phma@phma.optus.nu> <9311bbcb-5f93-4f92-bac1-e58512f58afd@t19g2000prd.googlegroups.com> Date: Wed, 20 Apr 2011 00:16:52 -0400 Message-ID: Subject: Re: [lojban] Re: Mathematical epsilon From: Alex Rozenshteyn To: lojban@googlegroups.com X-Original-Sender: rpglover64@gmail.com X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com: domain of rpglover64@gmail.com designates 209.85.216.176 as permitted sender) smtp.mail=rpglover64@gmail.com; dkim=pass (test mode) header.i=@gmail.com Reply-To: lojban@googlegroups.com Precedence: list Mailing-list: list lojban@googlegroups.com; contact lojban+owners@googlegroups.com List-ID: X-Google-Group-Id: 1004133512417 List-Post: , List-Help: , List-Archive: Sender: lojban@googlegroups.com List-Subscribe: , List-Unsubscribe: , Content-Type: multipart/alternative; boundary=20cf30334e85f1f50b04a151e40d --20cf30334e85f1f50b04a151e40d Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable I just realized: maybe {no ji'i ma'u} manages to express most of what I'm looking for... On Tue, Apr 19, 2011 at 5:39 PM, Alex Rozenshteyn wro= te: > It's not so much the mathematical notation. I have found, in the unusual > company I keep, that we utilize the concept of a number that takes any > finite positive real (or rational) value, but which is only of interest w= hen > it is arbitrarily small. It feels like I might have use for a PA which > embodies this concept. > > > 2011/4/19 djandus > >> Isn't this just an option of where to put description? You can use >> {ge'o.ebu}, and then describe it as positive, arbitrary, then state at >> the end of the proof (as is standard) that it approaches zero. It >> doesn't have to be in the name, which is part of the beauty of the >> proof -- it never matters that you are sending any variable to zero >> until the very end of the proof. That's just a matter of preference, >> though. You could have any number of names that could imply any of >> what is to come, be it a name for arbitrary variable versus controlled >> variables, positive versus negative, or numbers that are going to be >> sent to any particular value (possibly a subset of controlled >> variables). >> >> On that note, it would be very important /not/ to name epsilon as a >> number going to zero, unless the name means explicitly "by the end of >> this proof, this variable will be sent to zero by something (not >> necessarily me)". If it means "I am sending this variable to zero", >> then you are being inaccurate - epsilon is arbitrary, delta we send to >> zero, then we prove that sending delta to zero forces epsilon to zero. >> It /must/ be a mechanic of the proof that causes it. >> >> A side note: I happen to be saying this from a purely mathematical >> perspective, without having studied what Lojban already has available >> for mathematical notation. >> >> On Apr 19, 3:20 am, james riley wrote: >> > Strictly speaking, in epsilon-delta analysis, epsilon and delta are >> > any positive real. We only get interested in them as they get small. >> > >> > :) >> > >> > Cmacis >> > >> > 2011/4/19 Jonathan Jones : >> > >> > >> > >> > >> > >> > >> > >> > > On Mon, Apr 18, 2011 at 8:02 PM, Pierre Abbat >> wrote: >> > >> > >> On Monday 18 April 2011 20:09:21 Ian Johnson wrote: >> > >> > For the latter, what's wrong with just using {.ebu} or something, >> minus >> > >> > the >> > >> > irritating conflict between this name and Euler's constant? >> > >> > >> Euler's constant is called {te'o}. No conflict. >> > >> > >> Pierre >> > >> > >> -- >> > >> I believe in Yellow when I'm in Sweden and in Black when I'm in >> Wales. >> > >> > > It does conflict with the variable "e", however. There's {ge'o.ebu}, >> which >> > > /is/ "=CE=B5". >> > >> > > -- >> > > mu'o mi'e .aionys. >> > >> > > .i.a'o.e'e ko cmima le bende pe lo pilno be denpa bu .i doi.luk. mi >> patfu do >> > > zo'o >> > > (Come to the Dot Side! Luke, I am your father. :D ) >> > >> > > -- >> > > You received this message because you are subscribed to the Google >> Groups >> > > "lojban" group. >> > > To post to this group, send email to lojban@googlegroups.com. >> > > To unsubscribe from this group, send email to >> > > lojban+unsubscribe@googlegroups.com. >> > > For more options, visit this group at >> > >http://groups.google.com/group/lojban?hl=3Den. >> >> -- >> You received this message because you are subscribed to the Google Group= s >> "lojban" group. >> To post to this group, send email to lojban@googlegroups.com. >> To unsubscribe from this group, send email to >> lojban+unsubscribe@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/lojban?hl=3Den. >> >> > > > -- > Alex R > > --=20 Alex R --=20 You received this message because you are subscribed to the Google Groups "= lojban" group. To post to this group, send email to lojban@googlegroups.com. To unsubscribe from this group, send email to lojban+unsubscribe@googlegrou= ps.com. For more options, visit this group at http://groups.google.com/group/lojban= ?hl=3Den. --20cf30334e85f1f50b04a151e40d Content-Type: text/html; charset=ISO-8859-7 Content-Transfer-Encoding: quoted-printable I just realized:=A0 maybe {no ji'i ma'u} manages to express most of= what I'm looking for...

On Tue, Apr = 19, 2011 at 5:39 PM, Alex Rozenshteyn <rpglover64@gmail.com> wrote:
It's not so much the mathematical notat= ion.=A0 I have found, in the unusual company I keep, that we utilize the co= ncept of a number that takes any finite positive real (or rational) value, = but which is only of interest when it is arbitrarily small.=A0 It feels lik= e I might have use for a PA which embodies this concept.


2011/4/19 djandus <jandew@gmail.com><= /span>
Isn't this just an option of where to put description? You can use
{ge'o.ebu}, and then describe it as positive, arbitrary, then state at<= br> the end of the proof (as is standard) that it approaches zero. It
doesn't have to be in the name, which is part of the beauty of the
proof -- it never matters that you are sending any variable to zero
until the very end of the proof. That's just a matter of preference, though. You could have any number of names that could imply any of
what is to come, be it a name for arbitrary variable versus controlled
variables, positive versus negative, or numbers that are going to be
sent to any particular value (possibly a subset of controlled
variables).

On that note, it would be very important /not/ to name epsilon as a
number going to zero, unless the name means explicitly "by the end of<= br> this proof, this variable will be sent to zero by something (not
necessarily me)". If it means "I am sending this variable to zero= ",
then you are being inaccurate - epsilon is arbitrary, delta we send to
zero, then we prove that sending delta to zero forces epsilon to zero.
It /must/ be a mechanic of the proof that causes it.

A side note: I happen to be saying this from a purely mathematical
perspective, without having studied what Lojban already has available
for mathematical notation.

On Apr 19, 3:20=A0am, james riley <jimr1...@gmail.com> wrote:
> Strictly speaking, in epsilon-delta analysis, epsilon and delta are > any positive real. We only get interested in them as they get small. >
> :)
>
> Cmacis
>
> 2011/4/19 Jonathan Jones <eyeo...@gmail.com>:
>
>
>
>
>
>
>
> > On Mon, Apr 18, 2011 at 8:02 PM, Pierre Abbat <p...@phma.optus.nu> wrote:<= br> >
> >> On Monday 18 April 2011 20:09:21 Ian Johnson wrote:
> >> > For the latter, what's wrong with just using {.ebu} = or something, minus
> >> > the
> >> > irritating conflict between this name and Euler's co= nstant?
>
> >> Euler's constant is called {te'o}. No conflict.
>
> >> Pierre
>
> >> --
> >> I believe in Yellow when I'm in Sweden and in Black when = I'm in Wales.
>
> > It does conflict with the variable "e", however. There&= #39;s {ge'o.ebu}, which
> > /is/ "=E5".
>
> > --
> > mu'o mi'e .aionys.
>
> > .i.a'o.e'e ko cmima le bende pe lo pilno be denpa bu .i d= oi.luk. mi patfu do
> > zo'o
> > (Come to the Dot Side! Luke, I am your father. :D )
>
> > --
> > You received this message because you are subscribed to the Googl= e Groups
> > "lojban" group.
> > To post to this group, send email to lojban@googlegroups.com.
> > To unsubscribe from this group, send email to
> > lojban+unsubscribe@googlegroups.com.
> > For more options, visit this group at
> >http://groups.google.com/group/lojban?hl=3Den.

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--
=A0=A0 =A0 =A0 =A0 =A0Alex R=




--
=A0=A0 =A0 =A0 =A0 =A0Alex R

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