To solve the problem of identifying the subset of numbers that represents the set
[tex]\[ \left\{0.33, \pi(3.14159 \ldots), \frac{1}{4}, -23\right\}, \][/tex]
follow these steps:
1. Identify each number in the set:
- [tex]\(0.33\)[/tex]: This is a positive decimal number.
- [tex]\(\pi (3.14159 \ldots)\)[/tex]: This is a positive irrational number.
- [tex]\(\frac{1}{4}\)[/tex]: This is a positive fraction.
- [tex]\(-23\)[/tex]: This is a negative integer.
2. Classify each number according to its sign:
- [tex]\(0.33\)[/tex]: Positive
- [tex]\(\pi (3.14159 \ldots)\)[/tex]: Positive
- [tex]\(\frac{1}{4}\)[/tex]: Positive
- [tex]\(-23\)[/tex]: Negative
3. Select the subset specified by the problem:
The problem asks us to focus on "Negative numbers." From the classification above, the number that fits this criterion is:
- [tex]\(-23\)[/tex]
Thus, the most specific subset of all numbers to describe the negative numbers in the given set is:
[tex]\[ \{-23\} \][/tex]
