1. **State the problem:** Given the set \{5-9, -4, 5, 0, 0.25, 23, 9.2, 21006\}, classify each number into the categories: a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. 2. **Simplify the set:** Calculate 5-9 = -4, so the set is \{-4, -4, 5, 0, 0.25, 23, 9.2, 21006\} which simplifies to \{-4, 5, 0, 0.25, 23, 9.2, 21006\}. 3. **Define each category:** - Natural numbers: positive integers starting from 1 (\{1, 2, 3, ...\}) - Whole numbers: natural numbers plus zero (\{0, 1, 2, 3, ...\}) - Integers: all whole numbers plus negative integers (\{..., -3, -2, -1, 0, 1, 2, 3, ...\}) - Rational numbers: numbers expressible as a fraction $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$ - Irrational numbers: real numbers that are not rational - Real numbers: all rational and irrational numbers 4. **Classify each number:** - $-4$: integer, rational, real - $5$: natural, whole, integer, rational, real - $0$: whole, integer, rational, real - $0.25$: rational ($\frac{1}{4}$), real - $23$: natural, whole, integer, rational, real - $9.2$: rational ($\frac{92}{10}$), real - $21006$: natural, whole, integer, rational, real 5. **List numbers by category:** - a. Natural numbers: \{5, 23, 21006\} - b. Whole numbers: \{0, 5, 23, 21006\} - c. Integers: \{-4, 0, 5, 23, 21006\} - d. Rational numbers: \{-4, 0, 0.25, 5, 9.2, 23, 21006\} - e. Irrational numbers: none - f. Real numbers: all numbers in the set \{-4, 0, 0.25, 5, 9.2, 23, 21006\} **Final answer:** - Natural: $\{5, 23, 21006\}$ - Whole: $\{0, 5, 23, 21006\}$ - Integers: $\{-4, 0, 5, 23, 21006\}$ - Rational: $\{-4, 0, 0.25, 5, 9.2, 23, 21006\}$ - Irrational: $\emptyset$ - Real: $\{-4, 0, 0.25, 5, 9.2, 23, 21006\}$