Question

Can there be any property which exists in "Z" But not in "Q"? Why?

Answer 1

Set relations

• Integers. The set of all integers contains the whole numbers $0, \pm 1, \pm 2, \pm 3, ...$ and the set is denoted by $\mathbb{Z}$.

• Rational numbers. The set of all rational numbers contains the numbers of the form $\frac{a}{b}$ where both $a$ and $b$ are integers with $b\neq 0$ and the set is denoted by $\mathbb{Q}$.

• Relation between the set of integers and the set of rational numbers. We must know that the set of integers is a subset of the set of rational numbers, i.e., $\mathbb{Z}\subset\mathbb{Q}$.

Answer.

• There cannot be any property which exists in $\mathbb{Z}$ but not in $\mathbb{Q}$.

• The reason is simple. $\mathbb{Q}$ being the superset of $\mathbb{Z}$ satisfies all the properties of $\mathbb{Z}$.