> Shouldn't theorems be independent of arbitrary decisions regarding what is or > is not a prime number? Otherwise I'll have to believe that mathematicians > are just making up stuff.
Within a school of thought they are. Occasionally people make different assumptions about one thing or another (the axiom of choice for example) and two schools of proofs, with different assumption, arise. When writing such papers the author usually states these assumptions. Though it looks like primes have had an uncontested definition for a long period of time so I wouldn't worry about it. ( It would be interesting if someone could point out a paper where 1 was assumed a prime and it had mathematical consequences beyond incrementing an index. ) **************************** Greg Sonnenfeld On Sat, Dec 10, 2011 at 7:55 PM, Robert J. Cordingley <rob...@cirrillian.com> wrote: > Shouldn't theorems be independent of arbitrary decisions regarding what is > or is not a prime number? Otherwise I'll have to believe that > mathematicians are just making up stuff. > > > > On 12/10/11 4:08 PM, George Duncan wrote: > > Yes, it does depend on how you define prime BUT speaking as a > > mathematician > > it is good to have definitions for which we get interesting theorems, like > the unique (prime) factorization theorem that says every natural number has > unique prime factors, so 6 has just 2 and 3, NOT 2 and 3 or 2 and 3 and 1. > So we don't want 1 as a prime or the theorem doesn't work. > > statistician > > do a Bing or Google search on prime number and see what frequency of entries > define 1 as prime (I didn't find any). So from an empirical point of view > usage says 1 is not prime > > artist > > try Bing of Google images and see how many pretty pictures show 1 as prime. > I didn't see any. > > Cheers, Duncan > > On Sat, Dec 10, 2011 at 5:19 PM, Pamela McCorduck <pam...@well.com> wrote: >> >> I asked the in-house mathematician about this. When he began, "Well, it >> depends on how you define 'prime' . . ." I knew it was an ambiguous case. >> >> PMcC >> >> >> >> On Dec 10, 2011, at 5:12 PM, Marcos wrote: >> >>> On Thu, Dec 8, 2011 at 2:17 AM, Russell Standish <r.stand...@unsw.edu.au> >>> wrote: >>>> >>>> Has one ever been prime? Never in my lifetime... >>> >>> >>> Primes start at 2 in my world. There was mathematician doing a talk >>> once, and before he started talking, he checked his microphone: >>> >>> "Testing...., testing, 2, 3, 5, 7" >>> >>> That's how I remember. >>> >>> Mark >>> >>> ============================================================ >>> FRIAM Applied Complexity Group listserv >>> Meets Fridays 9a-11:30 at cafe at St. John's College >>> lectures, archives, unsubscribe, maps at http://www.friam.org >> >> >> >> ============================================================ >> FRIAM Applied Complexity Group listserv >> Meets Fridays 9a-11:30 at cafe at St. John's College >> lectures, archives, unsubscribe, maps at http://www.friam.org > > > > > -- > George Duncan > georgeduncanart.com > (505) 983-6895 > Represented by ViVO Contemporary > 725 Canyon Road > Santa Fe, NM 87501 > > Life must be understood backwards; but... it must be lived forward. > Soren Kierkegaard > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
