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**To**:**"tech-userlevel%netbsd.org@localhost" <tech-userlevel%netbsd.org@localhost>****Subject**:**Re: CVS commit: src/games/factor****From**:**Joerg Sonnenberger <joerg%britannica.bec.de@localhost>**- Date: Tue, 18 May 2010 20:41:49 +0200

On Tue, May 18, 2010 at 10:46:52AM -0700, Paul Goyette wrote: > Neither side has offered any authoritative sources for their > respective arguments. Since neither of the primary participants > appears to be a recognized authority on the subject, the entire > discussion is nothing more than "amusing". Please pick a random book in a math library and check the definition. I haven't bothered to name specific ones because I am only aware of the two definitions I gave. I know quite a lot of topics in math that don't have that much agreement, but I am simply not aware of anyone recognized authority to disagree with this. Too many results depend on the set of primes not including 1. But to answer the question that has been raised by the "forward thinking" crowd, this is the reason why the definitions exist as they are. Many of the current theorems involving primes either don't work for unit elements or are completely useless and obvious. In other words, they either wouldn't add understanding or would have to exclude the unit elements. An example for the former is the factor ring Z/pZ. With p==1, you get the special 0-ring, which is extremely boring as it contains only one element and all operations are constant. In that way it can even be harmful in some cases, as you can't pick 1 != 0. A more involved example of the latter is the earlier mentioned theorem about prime factorisation. The unique prime factorisation is a very powerful concept and hard to justify to give up. Note that when talking about Z, the uniqueness is down to equivalence of primes, e.g. it doesn't guarantee that you can't pick different signs for the individual primes, but it says that it is the only difference. The number of prime factors doesn't change and the absolute value doesn't either. Joerg

**Follow-Ups**:**Re: CVS commit: src/games/factor***From:*Denis Lagno

**References**:**Re: CVS commit: src/games/factor***From:*Joerg Sonnenberger

**Re: CVS commit: src/games/factor***From:*Aleksej Saushev

**Re: CVS commit: src/games/factor***From:*Joerg Sonnenberger

**Re: CVS commit: src/games/factor***From:*Aleksej Saushev

**Re: CVS commit: src/games/factor***From:*Joerg Sonnenberger

**Re: CVS commit: src/games/factor***From:*Aleksej Saushev

**Re: CVS commit: src/games/factor***From:*Kristaps Dzonsons

**Re: CVS commit: src/games/factor***From:*Aleksej Saushev

**Re: CVS commit: src/games/factor***From:*Paul Goyette

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