1 = 0,99........

[Bridge]

Yeah I saw the proof and I don't accept it. Lim n->inf 0.{00.....001} (n-1) = 0 is a loss of data. There is a trailing 1 there, it is just not calculable at this point. I don't give a shit whether it works according to the current system, the fact is mathematics require concrete rules to work, and there are no rules for infinitesimals at this time. Mathematics are not absolute, no matter how much you want them to be.

EDIT: You do realize you can prove anything if you violate Occam's Razor, right?

Lim n->inf 0.{00.....001} (n-1) = 0 is NOT a loss of data. It is proven through Archimedean Property .

I may not know as many fancy names as you do, but when I have something, and then suddenly I have nothing, I consider that a loss of data. End of story. Plus:

"An algebraic structure in which any two non-zero elements are comparable, in the sense that neither of them is infinitesimal with respect to the other, is said to be Archimedean."

0.00 … 1 is infinitesimal in regard to 0.