From lojban+bncCML0xpmUARCx5rPtBBoENiMJVg@googlegroups.com Mon Apr 18 19:28:18 2011 Received: from mail-wy0-f189.google.com ([74.125.82.189]) by chain.digitalkingdom.org with esmtp (Exim 4.72) (envelope-from ) id 1QC0fm-0000v6-Di; Mon, 18 Apr 2011 19:28:18 -0700 Received: by wya21 with SMTP id 21sf6723842wya.16 for ; Mon, 18 Apr 2011 19:28:07 -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=1EcFcbImxSEJUXyGKDnpcViOsELscywSZ4y9Hss7A7M=; b=zkCbNavMhQmr06KPNZFR8NYd/3x9w01dxY7Bc0938B4HMka+JJhzlOSvrWpcKVIhDK F7Y6za7YKqZVKYt8523vc7oI/rGG2Atn2I0rB5K9XxX721EYJk4+hwHRP0rkhMZxdD4K AAPdf2KUhK7r7dbfGMXxFd8Ff/+AZm1xmTWbc= 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=HYrxR5AXSKcsZ3D5CjFAeK/R4d+t0gBiXYR9v1g5xMTE7ARuE37vZUcMAIjuTzAhh/ vvgEKSaGo2k57/rRo36gYj6YIls/Pkxk1Uh9Kiw7WeYbtrRZbkcUVqJshWMQTLhg4TJy F9JRd6WY1LZxd7LmsH2J2Vyn0mphDALMbDbM0= Received: by 10.216.81.143 with SMTP id m15mr1592341wee.13.1303180081524; Mon, 18 Apr 2011 19:28:01 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.227.139.31 with SMTP id c31ls100880wbu.0.gmail; Mon, 18 Apr 2011 19:28:00 -0700 (PDT) Received: by 10.227.173.76 with SMTP id o12mr281194wbz.6.1303180080739; Mon, 18 Apr 2011 19:28:00 -0700 (PDT) Received: by 10.227.173.76 with SMTP id o12mr281193wbz.6.1303180080662; Mon, 18 Apr 2011 19:28:00 -0700 (PDT) Received: from mail-ww0-f44.google.com (mail-ww0-f44.google.com [74.125.82.44]) by gmr-mx.google.com with ESMTPS id e5si1739999wbi.6.2011.04.18.19.28.00 (version=TLSv1/SSLv3 cipher=OTHER); Mon, 18 Apr 2011 19:28:00 -0700 (PDT) Received-SPF: pass (google.com: domain of blindbravado@gmail.com designates 74.125.82.44 as permitted sender) client-ip=74.125.82.44; Received: by wwa36 with SMTP id 36so6417670wwa.1 for ; Mon, 18 Apr 2011 19:28:00 -0700 (PDT) MIME-Version: 1.0 Received: by 10.216.69.203 with SMTP id n53mr11142943wed.88.1303180080411; Mon, 18 Apr 2011 19:28:00 -0700 (PDT) Received: by 10.216.13.211 with HTTP; Mon, 18 Apr 2011 19:28:00 -0700 (PDT) In-Reply-To: References: Date: Mon, 18 Apr 2011 22:28:00 -0400 Message-ID: Subject: Re: [lojban] Mathematical epsilon From: Ian Johnson To: lojban@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 74.125.82.44 as permitted sender) smtp.mail=blindbravado@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=000e0ce0cdc8c5742c04a13c4155 --000e0ce0cdc8c5742c04a13c4155 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable In actually doing proofs in analysis, it is not at all uncommon to have a whole family of errors epsilon and distances delta and then take the minimu= m of all the deltas in order to simultaneously satisfy all the epsilons. (Thi= s is essentially how any "all but finitely many" situation is resolved.) Of course then you can subscript, just like we do in analysis. mu'o mi'e .latros. On Mon, Apr 18, 2011 at 9:28 PM, Alex Rozenshteyn wro= te: > I'm looking less for a symbol and more for a number, like {ci'i} or > {te'o}. I (holding the company that I do) have found myself using "epsil= on" > and meaning "an arbitrarily small number", and this seems like a number t= hat > would be useful. > > Also, I can't see a context where the two different infinitesimals would = be > confused (but I haven't done much analysis), so a single cmavo could > probably encompass both. > > > 2011/4/18 Ian Johnson > >> For the latter, what's wrong with just using {.ebu} or something, minus >> the irritating conflict between this name and Euler's constant? >> >> For the former, incidentally, {li fi'u ci'i} works although it's really >> not at the correct level of precision for nonstandard analysis. >> >> >> mu'o mi'e .latros. >> >> On Mon, Apr 18, 2011 at 7:32 PM, .arpis. wr= ote: >> >>> doi Ian >>> >>> The latter. >>> >>> >>> On Mon, Apr 18, 2011 at 7:31 PM, .arpis. w= rote: >>> >>>> The =CE=B5-=CE=B4 definition of a limit isn't the only use of =CE=B5 i= n this sense, >>>> although it's the most well known. Epsilon is used to represent an >>>> arbitrarily small number, the same way that p is used to represent a p= rime. >>>> >>>> >>>> 2011/4/18 Jonathan Jones >>>> >>>>> On Mon, Apr 18, 2011 at 2:35 PM, Alex Rozenshteyn < >>>>> rpglover64@gmail.com> wrote: >>>>> >>>>>> .i me'o .Epsilon bu lo'o se pilno ci'e da poi cmaci ku'o fi lo sinxa >>>>>> be lo namcu poi na'e jimte fi lo ka cmalu >>>>>> .i ma xu namcu valsi bau la lojban smuni simsa >>>>>> .i go'i fa zo so'u xu >>>>>> >>>>>> ni'o xe fanva zoi gy >>>>>> >>>>>> The symbol "epsilon" is sometimes used in math to represent an >>>>>> arbitrarily small number. Is there a number word in lojban that mean= s >>>>>> something similar? Is "so'u" such a word? >>>>>> >>>>>> gy >>>>>> -- >>>>>> Alex R >>>>>> >>>>> >>>>> As in the formal definition of limits? We'd need something for =CE=B4= , not >>>>> just =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. >>>>> >>>> >>>> >>>> >>>> -- >>>> mu'o mi'e .arpis. >>>> >>>> >>> >>> >>> -- >>> mu'o mi'e .arpis. >>> >>> -- >>> 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. >>> >> >> -- >> 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 > > -- > 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 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. --000e0ce0cdc8c5742c04a13c4155 Content-Type: text/html; charset=ISO-8859-7 Content-Transfer-Encoding: quoted-printable In actually doing proofs in analysis, it is not at all uncommon to have a w= hole family of errors epsilon and distances delta and then take the minimum= of all the deltas in order to simultaneously satisfy all the epsilons. (Th= is is essentially how any "all but finitely many" situation is re= solved.) Of course then you can subscript, just like we do in analysis.

mu'o mi'e .latros.

On Mon, Ap= r 18, 2011 at 9:28 PM, Alex Rozenshteyn <rpglover64@gmail.com> wrote:
I'm looking less for a symbol and more for a number, like {ci'i} or= {te'o}.=A0 I (holding the company that I do) have found myself using &= quot;epsilon" and meaning "an arbitrarily small number", and= this seems like a number that would be useful.

Also, I can't see a context where the two different infinitesimals = would be confused (but I haven't done much analysis), so a single cmavo= could probably encompass both.


2011/4/18 Ian Johnson <blindbravado@gmail.= com>
For the latter, what's wrong with just u= sing {.ebu} or something, minus the irritating conflict between this name a= nd Euler's constant?

For the former, incidentally, {li fi'u ci'i} works although it&= #39;s really not at the correct level of precision for nonstandard analysis= .


mu'o mi'e .latros.

On Mon, Apr 18, 2011 at 7:32 PM, .arpis. <rpg= lover64+jbobau@gmail.com> wrote:
doi Ian

The latter.


On Mon, Apr 18, 2011 at 7:31 PM, .arp= is. <rpglover64+jbobau@gmail.com> wrote:
The =E5-=E4 definition of a limit isn't the only use of =E5 in this sen= se, although it's the most well known. Epsilon is used to represent an = arbitrarily small number, the same way that p is used to represent a prime.=


2011/4/18 Jonathan Jones &= lt;eyeonus@gmail.com= >
On Mon, Apr 18, 2011 at 2:3= 5 PM, Alex Rozenshteyn <rpglover64@gmail.com> wrote:
.i me'o .Epsilon bu lo'o se pilno ci'e da poi cmaci ku'o fi= lo sinxa be lo namcu poi na'e jimte fi lo ka cmalu
.i= ma xu namcu valsi bau la lojban smuni simsa
.i go'i fa zo so'u = xu

ni'o xe fanva zoi gy

The symbol "epsilon" is somet= imes used in math to represent an arbitrarily small number. Is there a numb= er word in lojban that means something similar? Is "so'u" suc= h a word?

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

As in the formal definition of l= imits? We'd need something for =E4, not just =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 )

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--
mu'o mi'e .arpis.




--
mu'o mi'= e .arpis.

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

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