State whether the following statements are true or false. Justify your answer.
$(i)$ The number of rational numbers between $15$ and $18$ is finite.
$(ii)$ There are numbers which cannot be written in the form $\frac{p}{q}$,where $q \neq 0$ and $p, q$ are both integers.

(N/A) $(i)$ The statement is false. There are infinitely many rational numbers between any two distinct rational numbers. Therefore,the number of rational numbers between $15$ and $18$ is infinite.
$(ii)$ The statement is true. Numbers that cannot be expressed in the form $\frac{p}{q}$ (where $p, q$ are integers and $q \neq 0$) are called irrational numbers. For example,$\sqrt{2}$,$\sqrt{3}$,and $\pi$ are such numbers.