Name the subset(s) of the real numbers to which each number belongs to /144

Answer 1

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