🚀 go-pugleaf

In article <1992Aug12.194603.23527@news.th-darmstadt.de> graef@rs5.hrz.th-darmstadt.de (Ulrich Graef) writes:
>In article <1992Aug12.171656.8755@tessi.com>, george@tessi.com (George Mitchell) writes:
>> graef@rs5.hrz.th-darmstadt.de (Ulrich Graef) writes:
>> 
>> >You must notice, that there exists a small community (even with
>> >mathematicians among them) which does not believe in inductive
>> >proofs. I think, they have a lot of problems with commonly
>> >accepted theorems.
>> 
>> Whoa!  Euclid's proof does not involve induction!  It is a
>> reductio ad absurdum proof, ...
>
>You are right, but I only use the wrong words (english is not
>my native language). There is also a group, which worries
>about `reductio ad absurdum' proofs.
>
>A friend of mine worry about both!!!

But Euclid's proof can easily be rewritten as a totally constructive
proof, one that fulfils even the most stringent constructivist
demands. Of course, then it's no longer a proof that there is an
infinite number of primes (I suppose constructivists wouldn't accept
such a statemnet as meaningful, anyway), but a proof that given any 
(finite) list of primes, one can always construct a prime not on the
list. 

Magnus Olsson                   | \e+      /_
Dept. of Theoretical Physics    |  \  Z   / q
University of Lund, Sweden      |   >----<           
Internet: magnus@thep.lu.se     |  /      \===== g
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