Why should I switch to Python? - Infinity of Primes

David C. Ullrich ullrich at math.okstate.edu
Tue Apr 4 20:38:21 CEST 2000


    Seeing your name here for a second I was confused
whether I'd hit the sci.math button...

    There's nothing non-constructive about the traditional
proof of the infinitude of the sequence of primes - given
a sequence of primes it _constructs_ a prime not on the
list. (Of course it doesn't actually return infinitely many
primes in one calculation, but neither does any other
algorithm.) Could be that there's a proof of the existence
of infinitely many primes using FTA that has some property
not shared by Euclid's proof, but "constructive" isn't it.

Cameron Laird wrote:

> In article <8ccoug$f4o$1 at pegasus.csx.cam.ac.uk>,
> Nick Maclaren <nmm1 at cus.cam.ac.uk> wrote:
> >
> >In article <NDBBKEGCNONMNKGDINPFGEJDDFAA.infonuovo at email.com>, "Dennis E. Hamilton" <infonuovo at email.com> writes:
> >|> The standard approach is a proof by contradiction starting from the
> >|> assumption that there is a largest prime.
> >
> >There is also a constructive proof based on the Fundamental
> >Theorem of Arithmetic, that is little more complex.
>                         .
>                         .
>                         .
> To what extent are constructive proofs supplanting *... ad
> absurdum* as standards?  At about the time I left academe
> I was working on my own arguments that our conventional
> view of the former as "more complex" is, as Brouwer et al.
> taught, essentially only convention.  Tilting at construc-
> tivist windmills is one of the half-dozen careers I'm
> considering for my retirement; I recognize, though, that
> I've quite lost touch with current practice.
> --
>
> Cameron Laird <claird at NeoSoft.com>
> Business:  http://www.Phaseit.net
> Personal:  http://starbase.neosoft.com/~claird/home.html




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