Question
Are all rational numbers also whole numbers? Are all whole numbers also rational numbers?
Answers
GPT-4o mini
No, not all rational numbers are whole numbers. Rational numbers include any number that can be expressed as a fraction \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q \neq 0\). This includes fractions (like \(\frac{1}{2}\), \(-\frac{3}{4}\)), which are not whole numbers.
However, all whole numbers are rational numbers. Whole numbers are non-negative integers (0, 1, 2, 3, ...), and they can be expressed as a fraction with a denominator of 1 (for example, the whole number 3 can be expressed as \(\frac{3}{1}\)). Thus, whole numbers are indeed a subset of rational numbers.
However, all whole numbers are rational numbers. Whole numbers are non-negative integers (0, 1, 2, 3, ...), and they can be expressed as a fraction with a denominator of 1 (for example, the whole number 3 can be expressed as \(\frac{3}{1}\)). Thus, whole numbers are indeed a subset of rational numbers.