Question
are all rational numbers integers
Answers
GPT-4o mini
No, not all rational numbers are integers.
Rational numbers are defined as numbers that can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers, and \(b \neq 0\). This includes numbers like \(\frac{1}{2}\), \(-\frac{3}{4}\), and \(\frac{5}{1}\) (which is simply the integer 5).
Integers are a subset of rational numbers that include all whole numbers (both positive and negative) and zero, such as \(-3, -2, -1, 0, 1, 2, 3\).
Thus, while all integers are rational numbers (since they can be expressed as fractions with a denominator of 1), not all rational numbers are integers.
Rational numbers are defined as numbers that can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers, and \(b \neq 0\). This includes numbers like \(\frac{1}{2}\), \(-\frac{3}{4}\), and \(\frac{5}{1}\) (which is simply the integer 5).
Integers are a subset of rational numbers that include all whole numbers (both positive and negative) and zero, such as \(-3, -2, -1, 0, 1, 2, 3\).
Thus, while all integers are rational numbers (since they can be expressed as fractions with a denominator of 1), not all rational numbers are integers.