Question
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
Ask by Ryan Ayala. in South Africa
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
They are integers, which include whole numbers and their negative counterparts.
Solution
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.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
The numbers you're talking about are known as integers! They include all the positive whole numbers, zero, and the negative whole numbers, allowing for operations like subtraction of larger numbers from smaller ones. So, for example, when you do \(3 - 5\), you're stepping into the world of negative integers with the result of \(-2\). Integers play a crucial role in various real-world applications, such as in finance. Think about accounts with overdrafts where you can have a negative balance, which directly uses the concept of integers! They're also used in programming for keeping track of scores, temperatures, or levels where both positive and negative numbers are essential.
