No, Marcelo is not correct. The statement "rational numbers are integers" is not always true.
To understand this, we need to clarify the definitions of rational numbers and integers:
-
Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. For example, \( \frac{1}{2} \), \( \frac{-3}{4} \), and \( 5 \) (which can be expressed as \( \frac{5}{1} \)) are all rational numbers.
-
Integers are whole numbers that can be positive, negative, or zero. They include numbers like -2, -1, 0, 1, 2, etc.
While all integers are rational numbers (since any integer \( n \) can be written as \( \frac{n}{1} \)), not all rational numbers are integers. For example, the number \( \frac{1}{2} \) is a rational number but not an integer.
Therefore, a counterexample is \( \frac{1}{2} \), which demonstrates that not all rational numbers are integers.
1 answer