Answer
**Number Lines Explained:**
- **Natural Numbers:** Start at 1 and go right indefinitely.
- **Whole Numbers:** Start at 0 and go right indefinitely.
- **Integers:** Extend left and right from 0, including all whole numbers and their negatives.
These lines help visualize the different sets of numbers and how they relate to each other.
Solution
Certainly! Let's explore number lines for **Natural Numbers**, **Whole Numbers**, and **Integers**. Below are explanations and textual representations of each:
---
### a. **Natural Numbers**
**Definition:**
Natural numbers are the set of positive integers used for counting. They start at **1** and increase indefinitely:
**Natural Numbers = {1, 2, 3, 4, 5, ...}**
**Number Line Representation:**
```
0 1 2 3 4 5 6 7 ...
|-----|-----|-----|-----|-----|-----|-----|----->
```
**Explanation:**
- The number line starts at **1**, representing the first natural number.
- Arrows extend infinitely to the right, indicating that natural numbers continue without end.
- Only the positive side of the number line is used for natural numbers.
---
### b. **Whole Numbers**
**Definition:**
Whole numbers include all natural numbers **plus zero**. They are used for counting where zero is a valid value:
**Whole Numbers = {0, 1, 2, 3, 4, 5, ...}**
**Number Line Representation:**
```
... -2 -1 0 1 2 3 4 5 ...
|-----|-----|-----|-----|-----|-----|----->
```
**Explanation:**
- The number line starts at **0**, representing the inclusion of zero in whole numbers.
- Arrows extend infinitely to the right, showing that whole numbers continue without end.
- Only the non-negative side of the number line is used for whole numbers.
---
### c. **Integers**
**Definition:**
Integers include all whole numbers and their negative counterparts. They are used to represent values in both directions from zero:
**Integers = {..., -3, -2, -1, 0, 1, 2, 3, ...}**
**Number Line Representation:**
```
... -3 -2 -1 0 1 2 3 ...
|-----|-----|-----|-----|-----|-----|-----|-----|----->
```
**Explanation:**
- The number line includes both negative and positive numbers, extending infinitely in both directions.
- **0** is at the center, serving as the origin.
- Integers encompass all whole numbers and their negatives, providing a complete set for operations involving subtraction and negative values.
---
**Visual Summary:**
1. **Natural Numbers:** Start at **1** and go rightwards indefinitely.
2. **Whole Numbers:** Start at **0** and go rightwards indefinitely.
3. **Integers:** Extend infinitely in both left (negative) and right (positive) directions from **0**.
These textual number lines provide a clear understanding of how each set of numbers is positioned relative to one another on the number spectrum.
Reviewed and approved by the UpStudy tutoring team
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