Tuesday, July 31, 2001

 

Issue is factorization

What has become painfully clear in discussions on the newsgroup is that many of you that post in reply to my postings don't understand factorization.

Worse, of that same group, many of you are apparently confused by conventions like algebraic numbers or the FIELD of complex numbers versus complex number RINGS.

I've tried to guide you to a more general understanding by talking about fractions, and by demonstrating the use of the ring bridge, but I still get the feeling that most of you are still just sticking with what you know.

Ok, I'll just come out and say it without hinting:

I think most of you lack intellectual flexibility, logic, and mathematical rigor. That you have a sense of some mathematical understanding based on what you were taught, but that parrotlike you repeat it unable to do even simple extensions into territory that is somewhat new to you.

So what IS a factorization?

A factorization is just a statement that what's on both sides of the equal sign is the same thing.

12 = 3(4) because 3(4) = 3(4) and 3(4) = 12 = 3(2)(2).

(x+2)(x+2) = x^2 + 4x + 4 is another example.

What's so complicated about that?

Yet, some of you have been arguing strange things like, what if x is a complex number? Then couldn't "factors" be meaningless?

Factors can't be meaningless if a factorization exists, as long as x is in a ring

x+2 is a factor of x^2 + 4x + 4 PERIOD.

And it doesn't matter if I put the entire thing in the field of complex numbers, or in something funkier and say that x is an octonion!

x+2 will STILL be a factor of x^2 + 4x + 4 because (x+2)(x+2) = x^2 + 4x + 4.

Folks, this is basic math.

Now I've said to mathematicians in general that probably all you lose is prestige when it looks like the math community is denying something so simple, but hey, don't any of you care about the prestige of the math community?

Isn't there a single mathematician out there who isn't a little embarrassed to have people claiming they're mathematicians arguing against such truths on sci.math, who is willing to speak up to keep them from making you all look stupid?

Like I pointed out yesterday, a lot of these people posting apparently have nothing to lose. For some of them, this newsgroup is their chance to get a little attention, and they say stupid, rude or shocking things in attempts to get that attention.

But when it's clear that my proof is true, for reporters, that's news, and they are you.





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