I have a copy of Lehmer's prime table printed in 1956, and it indeed has 1 as the first prime. Rich ------- Quoting Charles Greathouse <charles.greathouse@case.edu>:
IANAA (I am not an algebraist) but as I understand it this is actually a rather Big Deal, that fields cannot have 1 = 0, and it's related to fields not being varieties. But I've never looked into it myself, I just trust that there is a reason...!
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Tue, Feb 4, 2014 at 11:11 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I think (0,+,*) ought to be considered a field. But apparently algebraists ignore it, I think by requiring that 1 != 0, probably to avoid having a special case.
--Dan
On 2014-02-04, at 8:00 PM, Henry Baker wrote:
Is {0,+,*} a field or not?
All of its non-zero elements have multiplicative inverses (vacuously) !
At 05:39 PM 2/4/2014, James Buddenhagen wrote:
Back in 1914 the number 1 was a prime. At least according to D. N. Lehmer. See D. N. Lehmer, List of primes numbers from 1 to 10,006,721, Carnegie Institution Washington, D.C., 1914
On Tue, Feb 4, 2014 at 1:38 PM, Andy Latto <andy.latto@pobox.com> wrote:
On Tue, Feb 4, 2014 at 2:12 PM, Eugene Salamin <gene_salamin@yahoo.com> wrote:
According to a friend who volunteers in the Santa Cruz CA Public Schools, the official view is that 1 is a prime, because its only divisors are 1 and itself. However, a teacher did mention that in more advanced mathematics, 1 is not a prime.
Do they also teach that unique factorization is false? Or is it stated as "numbers > 1 have a unique factorization into primes other than 1"?
Andy
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