Nonstandard analysis exists (with infinitesimal and infinite numbers) , but 1/3 and 9/9 is the same there. The problem is that the numbers 0.333... and 0.999...

Nonstandard analysis exists (with infinitesimal and infinite numbers) , but 1/3 and 9/9 is the same there. The problem is that the numbers 0.333... and 0.999... don't really exist.