Question

Which set of numbers is the largest family group that includes all of the others. Is it real numbers natural numbers irrational numbers are rational numbers.

Answer 1

To determine which set of numbers is the largest family group that includes all of the others, let's categorize them:

1. **Natural Numbers**: These are the numbers starting from 1 (1, 2, 3, ...) and do not include negative numbers, fractions, or decimals.

2. **Rational Numbers**: These include all numbers that can be expressed as a fraction of two integers (where the denominator is not zero). This set includes natural numbers, whole numbers, integers, and any fractions or terminating/repeating decimals.

3. **Irrational Numbers**: These are numbers that cannot be expressed as a fraction of two integers. Their decimal representations are non-terminating and non-repeating (like √2, π).

4. **Real Numbers**: This set includes all rational and irrational numbers. It encompasses natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Now, considering the inclusivity of these groups:

- Natural numbers are included in rational numbers.
- Rational numbers include all integers and natural numbers.
- Irrational numbers are not included in rational numbers but fall under the broader category of real numbers.
- Real numbers include all rational and irrational numbers.

Therefore, the largest family group that includes all of the others is **Real Numbers**.