On Thu, Dec 6, 2012 at 12:03 PM, Joe Niederberger <firstname.lastname@example.org> wrote: >>If he claims that the system he invents is a ring, then he is not telling the truth > > He (Martinez) didn't, so what is it? Keep addition as is, but be willing to change the usual rules of multiplication in order to impose the new sign rule: (-) x (-) = (-). >
As long as one does not lie about what is being done, one can do whatever one wants. That is, in mathematics, we can make any set of definitions we want and derive from them what we can, and if certain people in mathematics find it interesting, it gets published in a journal.
But this does not mean that anything that has been proved in a given system like a ring is no longer proved in that system. This means that since the familiar number systems like the complex numbers and its familiar subsets and other familiar systems based on such as matrix rings are examples of rings, what he is doing as no application at all in these systems - that is, none of it is true in these systems. He's working with a totally different set of elements. He is not working with complex numbers or its subsets, and he is not working with matrices in a matrix ring. It's ultimately just an idle exercise.
Keep in mind that he has no degree in mathematics, even at the undergraduate level. Go to Google and enter "Alberto A. Martínez" "curriculum vitae" (with quotation marks) and at one of the hits we find this:
Department of History University of Texas at Austin 1 University Station B7000 Austin, TX 78712-0220
Ph.D. University of Minnesota, Minneapolis, Major: History of Science and Technology; Minor: Philosophy of Science
M.A. New York University, Philosophy of Physics, Gallatin School, New York City (plus courses at Graduate School, City University of New York, and at Vassar College, New York
B.A. Universidad de Puerto Rico, Río Piedras, Puerto Rico, General Studies, magna cum laude