Which type of numbers in the number system are defined by the following? "Numbers that extend the natural and whole number systems by including the operation \( a-b \), where \( a

Ask by Ryan Ayala. in South Africa

Jan 24,2025

The type of numbers you're referring to are **integers**. ### Explanation: - **Natural Numbers**: These are the basic counting numbers starting from 1, 2, 3, and so on. - **Whole Numbers**: These include all natural numbers **plus zero** (0, 1, 2, 3, ...). - **Extending to Allow Subtraction \( (a - b) \) Where \( a < b \)**: - In the natural and whole number systems, subtracting a larger number from a smaller one (e.g., \( 3 - 5 \)) isn't possible within the system because it would result in a negative value, which isn't included in these systems. - To accommodate such operations, **integers** are introduced. Integers include all whole numbers **and their negative counterparts** (..., -3, -2, -1, 0, 1, 2, 3, ...). Thus, by extending natural and whole numbers to include negative values, the system becomes the set of **integers**. **Answer:** They are the integers, which include whole numbers and their negative counterparts.