A paper describing grossone used to measure such things as the sierpinski carpet here:http://arxiv.org/abs/1203.3150
I'd like to discuss the legitimacy of grossone. What is the general consensus in the mathematical world? Is it similar to the $\tau$ vs. $\pi$ debate that was entirely irrelevant? Or is it a legitimate solution to the long standing problems of calculations at infinity?
In the paper, he distinguishes between iterations of the sierpinski carpet, that are undistinguisable with the common notion of infinity.