0 \in N, 5 \in N => (0/5) \in Q. Therefore 0 \in Q. QED.
Given the definition "The definition of a rational number is a number that can be expressed as the quotient of two integers where the denominator is not 0."
Let N be the set of all integers and Q be the set of all rational numbers.
Trivially 0 is in the set N, 5 is in the set N
by the definition 0/5 is in Q. Therefore 0 is in Q. QED.