From lojban+bncCOib25n_BhCkgrjtBBoEJwD_pA@googlegroups.com Tue Apr 19 14:40:10 2011 Received: from mail-qy0-f189.google.com ([209.85.216.189]) by chain.digitalkingdom.org with esmtp (Exim 4.72) (envelope-from ) id 1QCIeO-0001aZ-Mu; Tue, 19 Apr 2011 14:40:09 -0700 Received: by qyk36 with SMTP id 36sf198791qyk.16 for ; Tue, 19 Apr 2011 14:39:54 -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=+Y+OAjG9aXcF59vZfQmWg1J3ffgWSSKZmAYhqbvmx2o=; b=u36/b++QG+ZztJD2SNWkLgVa6aQGs/t8KQsrkzGBOToFxN6uyTst+H7Ns6DRMJIZyW vyn6FSmevjl+VZdCIPTVPGFRFnH5jfB+N1eREd39hEh2Wk/GHkYhcquto2ZZyPGLEwY/ YxCgUgcwWlGQc0GbHItfFp1k4gnQGjCsvf6cs= 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=Uev/EKlRTsqVa6a0sSWgaLvEAvQm8jWwQ+t3RLXjn0vTJjnlvabGf2VbewpZjSfDYa SnFEIgfIszGL/0m5Z0QbHDams4KaVozO9SRCwnXI6cPo2lQv7Cz+30TB/D47PKpg/l77 rbwojpibpPkrhUaP3ULu64qZOvryHCPNY6YvM= Received: by 10.224.54.12 with SMTP id o12mr697075qag.36.1303249188109; Tue, 19 Apr 2011 14:39:48 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.224.217.73 with SMTP id hl9ls165063qab.1.gmail; Tue, 19 Apr 2011 14:39:47 -0700 (PDT) Received: by 10.224.205.69 with SMTP id fp5mr342578qab.25.1303249187462; Tue, 19 Apr 2011 14:39:47 -0700 (PDT) Received: by 10.224.205.69 with SMTP id fp5mr342577qab.25.1303249187433; Tue, 19 Apr 2011 14:39:47 -0700 (PDT) Received: from mail-qw0-f44.google.com (mail-qw0-f44.google.com [209.85.216.44]) by gmr-mx.google.com with ESMTPS id o12si56893qcu.10.2011.04.19.14.39.47 (version=TLSv1/SSLv3 cipher=OTHER); Tue, 19 Apr 2011 14:39:47 -0700 (PDT) Received-SPF: pass (google.com: domain of rpglover64@gmail.com designates 209.85.216.44 as permitted sender) client-ip=209.85.216.44; Received: by mail-qw0-f44.google.com with SMTP id 23so77450qwc.31 for ; Tue, 19 Apr 2011 14:39:47 -0700 (PDT) MIME-Version: 1.0 Received: by 10.224.33.76 with SMTP id g12mr4753774qad.376.1303249187179; Tue, 19 Apr 2011 14:39:47 -0700 (PDT) Received: by 10.224.28.203 with HTTP; Tue, 19 Apr 2011 14:39:47 -0700 (PDT) In-Reply-To: <9311bbcb-5f93-4f92-bac1-e58512f58afd@t19g2000prd.googlegroups.com> References: <201104182202.57948.phma@phma.optus.nu> <9311bbcb-5f93-4f92-bac1-e58512f58afd@t19g2000prd.googlegroups.com> Date: Tue, 19 Apr 2011 17:39:47 -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 209.85.216.44 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=20cf3074b5fedb0d5e04a14c58c4 --20cf3074b5fedb0d5e04a14c58c4 Content-Type: text/plain; charset=ISO-8859-7 Content-Transfer-Encoding: quoted-printable 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 whe= n 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 Wale= s. > > > > > It does conflict with the variable "e", however. There'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 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 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. > > --=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. --20cf3074b5fedb0d5e04a14c58c4 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable It's not so much the mathematical notation.=C2=A0 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= when it is arbitrarily small.=C2=A0 It feels like I might have use for a P= A which embodies this concept.

2011/4/19 djandus <jandew@gmail.com>
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=C2=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:
>
> >> 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/ "=CE=B5".
>
> > --
> > 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+u= nsubscribe@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 Groups &= quot;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/lojba= n?hl=3Den.




--
=C2=A0=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Alex R

--
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.
--20cf3074b5fedb0d5e04a14c58c4--