Concept guide
Arithmetic operations: whether the same inputs give a defined result in ℕ, ℤ and ℚ
Take a=3 and b=5. In each of the number systems ℕ (including 0), ℤ and ℚ, decide whether a+b, a·b, a−b and a÷b are defined; when they are, compute the result and decide which systems it belongs to. Then decide whether 3÷0 and 0÷0 are defined in these three systems.