---- Original message ---- >Date: Fri, 3 Mar 2006 19:04:32 -0800 (PST) >From: Reid Nichol <[EMAIL PROTECTED]> >Subject: Re: what is next? 3.10 or 4.0??? >To: Matthew Weigel <[EMAIL PROTECTED]> >Cc: misc@openbsd.org > >I find it interesting that you didn't send this entirely condisending >superior reply to the list. Now why is that? > > >--- Matthew Weigel <[EMAIL PROTECTED]> wrote: >> Reid Nichol wrote:
>> In "elementary number theory," "numbers" are usually the set of >> positive integers, including or not including 0 depending on >> circumstance. > >And you even use the usually. Perhaps you should check out the >definition of divisibility and what a divisor is before you make such a >comment. > >Even sticking to the positive integers if a divides b (written a|b) if >and only if there is an integer d such that ad=b. > >Notice the work integer in there. Notice the word positive is NOT in >there. > >So, -7 is a divisor of 7 because (-7)(-1)=7. We /must/ restrict the >divisors to positive numbers. Which is what the original poster didn't >do. > >Or didn't you notice that? > >And what does 0 (another special case) have to do with this >conversation? > using the "usual" definition of prime does require the restriction of potential divisors to the positive integers. this is because, historically, the postive integers were the ring over which number theorists worked, so one needn't consider negative integer divisors. if you'd like to do away with the confusion of such a definition, it's much easier to use the ideal-based definition of prime: http://en.wikipedia.org/wiki/Prime_ideal . note that i'm assuming commutative rings here. > >> #2: these definitions are fluid - by some definitions, '1' *is* >> prime, and by others it isn't. The question really depends on a >> particular mathematical writer's view, because it really has no >impact >> on the interesting results of "elementary number theory." > >Really. Point to a reference. Because the wikipedia and mathworld >agree with my definition. Not to mention all my professors and every >text that I've come across. > right on, reid! under no circumstances should 1 be considered a prime number: the ideal generated by 1, (1), is obviously not a prime ideal. > >> #3: you are a lot more condescending than your demonstrated knowledge >> warrants. reid is totally in the right. i didn't sense much condescension, just dropping definitions and such, like any respectable student of mathematics would and should do. cheers, jake
