Subjects mathematics

Number Classification F491D1

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Stating the problem:** We need to determine who is correct between Sammy and Vivian regarding the classification of the number 3 in terms of natural, whole, integer, and rational numbers. 2. **Definitions:** - Natural numbers are the set of positive integers starting from 1, i.e., $\{1, 2, 3, \ldots\}$. - Whole numbers are natural numbers including zero, i.e., $\{0, 1, 2, 3, \ldots\}$. - Integers include all whole numbers and their negatives, i.e., $\{\ldots, -2, -1, 0, 1, 2, \ldots\}$. - Rational numbers are numbers that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. 3. **Analyzing Sammy's statement:** Sammy says 3 is a whole number, so it is also an integer and rational. Since 3 is indeed a whole number (it is in $\{0,1,2,3,\ldots\}$), it is also an integer and rational number. Sammy's statement is correct. 4. **Analyzing Vivian's statement:** Vivian says 3 is a natural number, so it is also whole, integer, and rational. Since 3 is a natural number (it is in $\{1,2,3,\ldots\}$), it is also a whole number (natural numbers are a subset of whole numbers), an integer, and rational. Vivian's statement is also correct. 5. **Conclusion:** Both Sammy and Vivian are correct because 3 belongs to all these sets: natural, whole, integer, and rational numbers. **Final answer:** Both Sammy and Vivian are correct.