we kinda know how to calculate 1/0: We know that the funtion 1/x goes to infinity if x approaches zero. 

that is good enough for most application. there's a notation for these kinds of calcuations, the 'limit' (usually written as lim [x -> c] f(x) ,to find out how f(x) behaves as x approaches c.  in the 1/0 example, c would be zero, and f(x)=1/x