What I wanted to say is that for every set of numbers (natural, integer, rational, real,...) we want to discuss, some possible 'operations' are defined
The type of operation "division by zero" is not defined in any operation of any numerical system, at least if we remain in the field of classical mathematics
Then in reality, some calculators can return values (for ex. Ieee754 return infinite positive o infinite negative), even if most return a specific error precisely the infamous 'division by zero'