There seems to be a lot of mathematical issues with what I have seen so far out of the set of papers on this site. The rigidity has been thrown out the window in some of the papers. Most of my concerns have been found here:

http://forums.xkcd.com/viewtopic.php?t=57691&p=2050100

http://link.springer.com/article/10.1007%2Fs11202-008-0082-0

http://math.stackexchange.com/questions/122080/grossone-the-arxiv-blogs-pick-of-the-day

I like the idea but it seems far too widened to be true. It would seem reasonable if restricted to strictly naturals and in systems that are total (always decidable), but have lots to work still before I'd consider it well-defined.