From jjllambias2000@yahoo.com.ar Mon Aug 23 09:17:49 2004 Received: with ECARTIS (v1.0.0; list lojban-beginners); Mon, 23 Aug 2004 09:17:49 -0700 (PDT) Received: from web41906.mail.yahoo.com ([66.218.93.157]) by chain.digitalkingdom.org with smtp (Exim 4.34) id 1BzHW0-0005GO-SY for lojban-beginners@chain.digitalkingdom.org; Mon, 23 Aug 2004 09:17:49 -0700 Message-ID: <20040823161720.89788.qmail@web41906.mail.yahoo.com> Received: from [200.49.74.2] by web41906.mail.yahoo.com via HTTP; Mon, 23 Aug 2004 09:17:20 PDT Date: Mon, 23 Aug 2004 09:17:20 -0700 (PDT) From: Jorge "Llambías" Subject: [lojban-beginners] Re: logical proofs? To: lojban-beginners@chain.digitalkingdom.org In-Reply-To: <20040823153053.GI3257@chain.digitalkingdom.org> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-archive-position: 720 X-Approved-By: jjllambias2000@yahoo.com.ar X-ecartis-version: Ecartis v1.0.0 Sender: lojban-beginners-bounce@chain.digitalkingdom.org Errors-to: lojban-beginners-bounce@chain.digitalkingdom.org X-original-sender: jjllambias2000@yahoo.com.ar Precedence: bulk Reply-to: lojban-beginners@chain.digitalkingdom.org X-list: lojban-beginners --- Robin Lee Powell wrote: > On Mon, Aug 23, 2004 at 03:18:49AM -0400, Andrew Archibald wrote: > > > > Proof that there are infinitely many prime numbers: > > ni'o jarco lo du'u ci'i mulna'usle cei broda cu zasti I suggest {jarco lo du'u ci'i da mulna'usle}. Otherwise, I would be tempted to ask {xo mulna'usle naku zasti}, "how many are the primes that don't exist"? > > Suppose that we have a finite list of prime numbers. > > .i sruma lo du'u mi'o ponse lo liste be me'i ci'i broda > > (This relies on a certain amount of listener generosity for "me'i ci'i"; > "ci'i nai" is another possibility.) I like {me'i ci'i} for finite, but {ponse}? In what sense do we own the list? I'd just say: {ru'a fo'a liste me'i ci'i broda} > > Then construct the number that is one greater than the product of all > > the prime numbers in the list. > > .i ba bo finti ko'a goi lo namcu poi ve jmina li pa lo simxu pilji be ro > le se liste i ca'e ko'a sumji li pa lo simpi'i be ro lu'a fo'a > > This number is, by a previous result (you could prove it if you > > wanted), guaranteed to be divisible by some prime number - perhaps > > itself. > > .i ko'a to se nibli lo pu nu jarco toi cu kakne lo nu fendi fi pa > broda goi ko'e to cumki lo nu du ko'a toi i ko'a sei lo pu nu jarco cu nibli cu mulpi'i su'o broda goi ko'e no'u ju'ocu'i ko'a mulpi'i: x1 pilji x2 x3 ije x1 e x2 e x3 mulnau i.e. "x1 is divisible by x2" > > But the number is not divisible by any of the numbers in our finite > > list of primes, so there must be at least one prime not on the list > > (although it may not be the new number). > > .i ku'i ko'e na se fendi fi lo se liste broda .i se ni'i bo su'o broda > poi na se list cu zasti to cumki lo nu na du ko'a toi i ku'i ko'a na mulpi'i su'o lu'a fo'a i se ni'i bo su'o broda noi ju'ocu'i na du ko'a cu na se liste fo'a > > So no finite list can contain all the prime numbers. > > .i se ni'i bo lo liste be me'i ci'i broda cu na kakne lo nu vasru ro > broda i seni'ibo no liste be me'i ci'i broda cu liste ro broda > .i fe'o > > (fe'o seemed about right for the arrogance of QED :-) > > > If you'd like this a little more self-contained (you'll still need to > > depend on some properties of multiplication, addition, and ordering of > > the natural numbers) you can prepend the definition of a prime number: > > a natural number (i.e., positive integer) such that it can be written > > as a product of natural numbers in exactly one way, as one times > > itself. > > da poi mulna'usle cei broda cu ma'u zei mulna'u gi'e mulna'u pilji po'o > pa da Only "1" is mulna'u pilji pa da, all other primes have exactly two natural divisors. mu'o mi'e xorxes __________________________________ Do you Yahoo!? Yahoo! Mail Address AutoComplete - You start. We finish. http://promotions.yahoo.com/new_mail