a) That solution is sometimes implanted. The problem is: its slow, very, very, slow. It is not nearly as fast as regular integer arithmetic. (Also, +, -, /, and * aren't called axioms.) Also, how do you handle things such as powers and exponentiation (especially non-integer arguments)?

b) Search up for "BigInt libraries". The problem is the same with the others, its slow. You still have to allocate memory and the operations aren't as fast. However, BigInt libraries are widely used when necessary.