From lojban+bncCJzE7b_XFxCC8bftBBoEjFKfHg@googlegroups.com Tue Apr 19 14:03:21 2011 Received: from mail-px0-f189.google.com ([209.85.212.189]) by chain.digitalkingdom.org with esmtp (Exim 4.72) (envelope-from ) id 1QCI4k-0006zq-7n; Tue, 19 Apr 2011 14:03:20 -0700 Received: by pxi19 with SMTP id 19sf35204pxi.16 for ; Tue, 19 Apr 2011 14:03:04 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=beta; h=domainkey-signature:x-beenthere:mime-version:date:in-reply-to:x-ip :references:user-agent:x-http-useragent:message-id:subject:from:to :x-original-sender:reply-to:precedence:mailing-list:list-id :x-google-group-id:list-post:list-help:list-archive:sender :list-subscribe:list-unsubscribe:content-type :content-transfer-encoding; bh=tdujXxyemFK0PRkb10OkAyFlxz/TzqGPhCmheuiFXsM=; b=stz3HA+AoWWOhGmcDFwcBCERAAVmFn8crcFOgN1CKYUIAJP2ai3h6TUt5ar1ncvw+I IKL9EgvuXnCjQ+uLYRso0cR/oqyW3tG4bthiR0gcUtg+qd6dpXkhOQxD3AYYYIFAlwe3 kIozhcvSJ6tjOIUFL/NBv+J2/U/0q8N/QqC0w= DomainKey-Signature: a=rsa-sha1; c=nofws; d=googlegroups.com; s=beta; h=x-beenthere:mime-version:date:in-reply-to:x-ip:references :user-agent:x-http-useragent:message-id:subject:from:to :x-original-sender:reply-to:precedence:mailing-list:list-id :x-google-group-id:list-post:list-help:list-archive:sender :list-subscribe:list-unsubscribe:content-type :content-transfer-encoding; b=bh43pqgX2BWiAX6ojGhYtfc7Vq/Ex+n1bodY0kwPfOeMKyfuU3JaDcFeI1rHQDpuLv g0vGhAR0bBYkQyNYQZ/zuprPRfIYmp9gOCDOWiSjSR4rSe3teXbxwRhvjuwlsrB+n65W 7d16aOPYY9jfz7S4UYk2Jw8s87S+ULDquPi6Q= Received: by 10.68.7.230 with SMTP id m6mr770910pba.9.1303246978326; Tue, 19 Apr 2011 14:02:58 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.68.1.5 with SMTP id 5ls1659567pbi.1.gmail; Tue, 19 Apr 2011 14:02:57 -0700 (PDT) MIME-Version: 1.0 Received: by 10.68.20.199 with SMTP id p7mr381543pbe.39.1303246977392; Tue, 19 Apr 2011 14:02:57 -0700 (PDT) Received: by t19g2000prd.googlegroups.com with HTTP; Tue, 19 Apr 2011 14:02:57 -0700 (PDT) Date: Tue, 19 Apr 2011 14:02:57 -0700 (PDT) In-Reply-To: X-IP: 128.42.220.185 References: <201104182202.57948.phma@phma.optus.nu> User-Agent: G2/1.0 X-HTTP-UserAgent: Mozilla/5.0 (Windows; U; Windows NT 6.1; en-US) AppleWebKit/534.16 (KHTML, like Gecko) Chrome/10.0.648.205 Safari/534.16,gzip(gfe) Message-ID: <9311bbcb-5f93-4f92-bac1-e58512f58afd@t19g2000prd.googlegroups.com> Subject: [lojban] Re: Mathematical epsilon From: djandus To: lojban X-Original-Sender: jandew@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: text/plain; charset=ISO-8859-7 Content-Transfer-Encoding: quoted-printable 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=A0am, 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 wrot= e: > > >> On Monday 18 April 2011 20:09:21 Ian Johnson wrote: > >> > For the latter, what's wrong with just using {.ebu} or something, mi= nus > >> > 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}, wh= ich > > /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 pat= fu 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 Grou= ps > > "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 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.