Joerg Sonnenberger <joerg%britannica.bec.de@localhost> writes: > On Tue, May 18, 2010 at 01:50:01AM +0400, Aleksej Saushev wrote: >> Joerg Sonnenberger <joerg%britannica.bec.de@localhost> writes: >> >> > On Tue, May 18, 2010 at 12:35:16AM +0400, Aleksej Saushev wrote: >> >> >> It is easy to see that there exist numbers >> >> >> which occur in any their factorization. These are called "prime" >> >> >> numbers. >> >> > >> >> > That's not the definition of prime elements algebra uses, which is the >> >> > relevant field here. The algebraic definition of prime explicitly >> >> > excludes units. >> >> >> >> There's no algebra here, it is arithmetics, algebra may be relevant here, >> >> but it isn't to a large extent. >> > >> > The arithmetic definition of prime doesn't agree with you either. >> >> Who told that? Please, avoid referring to "I was taught this way and >> refuse to learn anything else." What is the basis under definition you use? > > I gave my definitions. I have no clue where you get yours from. All you > are doing is "There are other ways to define this". The two definitions > I gave and which you continue to ignore are those accepted in the field > of math. One of them is the fundation of classic arithmetics, the other > of modern number theory. I have seen no reason why using "Saushev > primes" would be better. You have never given neither definition nor rationale for it except references to some unknown authority, everything you have done so far is you have shown your faithful commitment into what you were told ex cathedra. I repeat once again, bring definition _and_ rationale behind it, definition without rationale isn't what we talked here before you single-handedly decided to coerce everyone to accept your point of view using advantage of the first move. The latter relates to what I pointed in my reply to commit message. You seem to lack understanding that there exist different schools in mathematics and in teaching mathematics, and some do teach it differently. They use different definitions and focus on different aspects. I know at least one school that doesn't teach mathematical analysis using Cauchy-style definitions prefering to start from topology, I know another (quite large!) school that introduces filters as soon as possible to avoid dealing with handful of special cases, I was taught Robinson (non-Archimedean) analysis in parallel to classical one. And as far as I remember there do exist schools that consider 1 as prime number. Note that I didn't proclaim this ex cathedra and performed some analysis of this possibility, while you didn't dare to bring anything to support your point of view. Note that both definitions of limit, the one based on filter bases and the topological one subsume classical definition and both operate completely different terms. Robinson definitions operate in quite another reality where exist infinitesimals and infinities, the very objects rejected by classical analysis. >> You have stripped part of question to make it easier to attack. >> I didn't hear any rationale for your rejection of 1 and 0 as prime numbers. >> I count it as you don't have any. > > See above. I stripped away all the irrevelant parts as they are not even > worth discussing as long as there is no agreement on the most basic > properties of the topic in question. They may seem irrelevant to you, but I don't consider them irrelevant. Facts stay as they were: 1. You tend to act well before controversial point is discussed, let alone settled. 2. You ignore anyone else who have different opinion. This happens even when what we discuss is a toy. -- HE CE3OH...
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