State whether the following statements are true or false. Justify your answer.
$(i)$ $\frac{\sqrt{2}}{3}$ is a rational number.
$(ii)$ There are infinitely many integers between any two integers.

(FALSE, FALSE) $(i)$ The given statement is false. $A$ rational number is defined as a number that can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$. Here,$\frac{\sqrt{2}}{3}$ has $p = \sqrt{2}$,which is an irrational number,not an integer. Therefore,$\frac{\sqrt{2}}{3}$ is an irrational number.
$(ii)$ The given statement is false. By definition,integers are whole numbers (...,$-2, -1, 0, 1, 2, ...$). Between any two consecutive integers,such as $3$ and $4$,there are no other integers.