R is a ring (specifically an integral domain), not \mathbb{R}. Sorry! Sincerely, Adam P. Goucher
----- Original Message ----- From: Andy Latto Sent: 02/10/14 02:26 PM To: math-fun Subject: Re: [math-fun] More 4th grade math
On Mon, Feb 10, 2014 at 5:45 AM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Well, the official definition of `prime' is `for all a,b in R, we have p|ab <==> (p|a or p|b)'.
What do you mean in R by x|y?
If you mean that there's a z in R such that xz = y, then x|y as long as x is nonzero, and every nonzero number is prime.
If you mean there's a z in X such that xz = y, then 2 is not prime (and neither is anything else), because 2 | 2pi * 1/pi, but does not divide either 2pi or 1/pi.
If you meant Z when you said R, then 1 is prime by your definition, since for any a and b, both sides of your equivalence are true.
If you want people to use a sensible definition of prime, you have to have them deal with the more complicated world where there aren't just primes and composites, but 4 types of numbers: 0, units, primes and composites.
Do the people who say that 1 is a prime also say that 0 is a composite?
Andy
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