Dopefish wrote:(That said, a link to his full work in Serbian has been provided, so perhaps if there's any capable Serbian speaking mathematicians around they could look it over and let us know if there's anything to it.)

I might get around to it eventually.

kumarevo wrote:The current mathematics: know the line only in this form

does not recognize these forms of

I think his theorems are out to solve this problem (if you look back at his older post, the first image is of regular lines, while the second is of lines that diverges into 2 or more lines). Which I think isn't really a problem with the mathematics we know now. It just might not look nice, and they're not functions.

I don't know if it's proper to use union like this, but wouldn't something like (y = x^2) U (y = x, x < 1) be an example of diverging curves? Or y = +-x^.5 - x^2? Or we can just treat those curves as separate non-diverging curves and just use what we know on both of them.

Really we already do that in a lot of modern mathematics, e.g. finding the intersect of two lines, finding the area between curves.

Also my thoughts on the "Natural line": It seems rather shaky. Essentially you're saying a line only has 2 points, the starting point and the end point. Say you have 2 lines, AB and BC, then you can connect them to make AC. Now is AC a natural line? If yes, that means I can cut down a natural line into smaller natural lines (If AC can be cut down to AB, AB can be cut down into something smaller). Basically then I can keep cutting down on the natural line until I have only the point A. That means within any natural line, there are an infinte number of points, which describes a regular line, and also runs counter to your axiom. So if AC is not a natural line, is it not possible to produce the line AC without the existence of point B?

Anyways, I don't think I'm willing to try to understand your 'alternative math' until I see at least one application of it. Can you provide a problem that your alternative math can solve that current math cannot?

EDIT: Just fixed up the quote to have the images