Sunday, December 21, 2008


JSH: Was never a factor argument

Now isn't that amazing, I go to the complex plane and can give an example like

7(x^2 + 3x + 2) = (7x + 7)(x + 2)

and posters who arrogantly argued with me for years, convincing untold numbers of people that I was wrong here fall apart just because I'm forcing the issue that the equations are in the field of complex numbers.

But factor arguments don't matter on the complex plane!!!

Yup. You're right, as I never had a factor argument. I've had a distribution argument.

So you can see how the 7 distributes through the factorization of x^2 + 3x + 2. That is about the distributive property.

Now going to a slightly more complex example STILL on the complex plane

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

is actually in all key respects the same as the factorization above!!!

Normalizing using a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, you get

7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2)

where b_1(0) = 0, b_2(0) = 0, which looks a lot more like

7(x^2 + 3x + 2) = (7x + 7)(x+2)

and it's still a DISTRIBUTION argument and I remind you are in the FIELD of complex numbers!!!

Without factor arguments available, the once derisive posters who arrogantly told you for years that I was wrong have no mathematical tools to distract, have no "counter examples", and in fact have nothing at all but their basic denial.

They were wrong.

They are wrong.

If mathematical society is tired of the field of complex numbers then fine, you keep acting like you have now for six years, but don't pretend that you are actually mathematicians or actually doing valid mathematics.

You are practicing your religion. And you don't give a damn about what is actually true.

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