Question
Which set of rational numbers is always rational?
Answers
GPT-4o mini
A set of rational numbers that is always rational is the set of all rational numbers themselves. This includes any number that can be expressed as the quotient of two integers, where the denominator is not zero.
Additionally, some specific operations on rational numbers can also produce rational numbers:
1. **Sum of two rational numbers**: The sum of any two rational numbers is always rational.
2. **Difference of two rational numbers**: The difference of any two rational numbers is always rational.
3. **Product of two rational numbers**: The product of any two rational numbers is always rational.
4. **Quotient of two rational numbers**: The quotient of any two rational numbers (where the second number is not zero) is always rational.
Therefore, any operation performed on a set of rational numbers (as long as it adheres to these rules) will result in rational numbers.
Additionally, some specific operations on rational numbers can also produce rational numbers:
1. **Sum of two rational numbers**: The sum of any two rational numbers is always rational.
2. **Difference of two rational numbers**: The difference of any two rational numbers is always rational.
3. **Product of two rational numbers**: The product of any two rational numbers is always rational.
4. **Quotient of two rational numbers**: The quotient of any two rational numbers (where the second number is not zero) is always rational.
Therefore, any operation performed on a set of rational numbers (as long as it adheres to these rules) will result in rational numbers.