Well, in my universe 1+1=10 as often as not. As for maths not coping with infinitesimals, I suggest reading about Gregor Cantor. He went barmy, but not before he'd proved that lemniscatological* infinity is only the first sort of infinity. He called it Aleph-Null, perhaps because all the Roman and Greek letters were taken already, or perhaps for fun. There is at least one other sort of infinity, that is in some sense "bigger" than Aleph-Null, and he suspected (but couldn't prove) that there are (is?) an infinite number of types of infinity. As far as I can make out, none of the infinities are (is?) very useful, except that they suggest there is (are?) an infinite number of types of infinitesimals.... arse.
As for the Planck limit itself, that's mainly of interest to pirates and their victims.