Re: [PrimeNumbers] Re: Hypothesis Part 2
> ... Yes indeed, the sign restriction was just to make theActually, Chris, the word "pedantic" was wrong on my part, as it
> statement easier. Pedantic perhaps, but as author of the page in
> question (not the theorem!!!) I'd offer another
> reason: laziness (or should I say simplicity).
may have a negative connotation, which was certainly not intended.
My intent was to say that by restricting the parameters to positive
integers, you have "over-specified" the theorem -- that's not a bad
thing at all, and certainly well justified since it avoids having
to answer the question of whether a negative integer can be prime.
> thing at all, and certainly well justified since it avoids havingWhy avoid it at all? The integers can be divided into four classes
> to answer the question of whether a negative integer can be prime.
which are relevant in this context.
1) Zero (the additive identity)
2) Units (1 and -1, the integers with norm equal to the multiplicative
3) Primes (those integers all of whose divisors with a smaller norm are
4) Composites (everything else).
As the integers form a unique factorization domain we don't have to
worry about concepts such as prime ideals.