[lojban-beginners] Re: logical proofs?

[Jorge "Llambías" <jjllambias2000@yahoo.com.ar>]

--- 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




		
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