Question
Name the subset(s) of the real numbers to which each number belongs to /144
Answers
Answered by
GPT-4o mini
To classify the number \(-144\) within subsets of real numbers, we can consider the following categories:
1. **Natural Numbers**: Positive integers starting from 1 (e.g., 1, 2, 3, ...). \(-144\) is **not** a natural number.
2. **Whole Numbers**: Non-negative integers (e.g., 0, 1, 2, 3, ...). \(-144\) is **not** a whole number.
3. **Integers**: All whole numbers and their negative counterparts (e.g., ..., -3, -2, -1, 0, 1, 2, 3, ...). \(-144\) **is** an integer.
4. **Rational Numbers**: Numbers that can be expressed as the quotient of two integers (e.g., \( \frac{a}{b} \) where \( b \neq 0 \)). \(-144\) can be expressed as \( \frac{-144}{1} \), so it **is** a rational number.
5. **Irrational Numbers**: Numbers that cannot be expressed as a simple fraction (e.g., \(\sqrt{2}\), \(\pi\)). \(-144\) is **not** an irrational number.
6. **Real Numbers**: All numbers on the number line, including both rational and irrational numbers. \(-144\) **is** a real number.
In summary, \(-144\) belongs to the following subsets of real numbers:
- Integers
- Rational Numbers
- Real Numbers
1. **Natural Numbers**: Positive integers starting from 1 (e.g., 1, 2, 3, ...). \(-144\) is **not** a natural number.
2. **Whole Numbers**: Non-negative integers (e.g., 0, 1, 2, 3, ...). \(-144\) is **not** a whole number.
3. **Integers**: All whole numbers and their negative counterparts (e.g., ..., -3, -2, -1, 0, 1, 2, 3, ...). \(-144\) **is** an integer.
4. **Rational Numbers**: Numbers that can be expressed as the quotient of two integers (e.g., \( \frac{a}{b} \) where \( b \neq 0 \)). \(-144\) can be expressed as \( \frac{-144}{1} \), so it **is** a rational number.
5. **Irrational Numbers**: Numbers that cannot be expressed as a simple fraction (e.g., \(\sqrt{2}\), \(\pi\)). \(-144\) is **not** an irrational number.
6. **Real Numbers**: All numbers on the number line, including both rational and irrational numbers. \(-144\) **is** a real number.
In summary, \(-144\) belongs to the following subsets of real numbers:
- Integers
- Rational Numbers
- Real Numbers