Question

Marcelo claims that the statement "rational numbers are integers" is ALWAYS true.Is Marcelo correct?If yes, explain why.If no, provide an example.

Answer 1

Marcelo is incorrect. The statement "rational numbers are integers" is not always true.

Rational numbers are defined as numbers that can be expressed as the quotient of two integers, where the denominator is not zero. This means that any rational number can be written in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).

However, integers are a specific subset of rational numbers that can be expressed in the form \( \frac{a}{1} \) (where \( b = 1 \)). Not all rational numbers meet this criterion.

For example, the rational number \( \frac{1}{2} \) is not an integer, as it cannot be expressed as a whole number. Thus, \( \frac{1}{2} \) is a rational number, but it is not an integer.

Therefore, while all integers are rational, not all rational numbers are integers, which disproves Marcelo's claim.