**Integers** are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. The set of integers is often denoted by the symbol **ℤ**, which comes from the German word *Zahlen* (meaning "numbers").

### Key Properties of Integers:
1. **Positive Integers:** These are numbers greater than zero (e.g., 1, 2, 3,...).
2. **Negative Integers:** These are numbers less than zero (e.g., -1, -2, -3,...).
3. **Zero:** This is considered an integer but is neither positive nor negative.
4. **Closed under Addition and Multiplication:** The sum or product of any two integers is also an integer.
5. **Not closed under Division:** Dividing two integers does not always result in an integer (e.g., 1 ÷ 2 = 0.5, which is not an integer).

### Set Representation:
- The set of integers can be written as:
  \[
  \mathbb{Z} = \{ ..., -3, -2, -1, 0, 1, 2, 3, ... \}
  \]

Would you like more details or have any specific questions about integers?

Here are 5 related questions to further explore the concept:
1. What are the differences between integers and rational numbers?
2. How do operations like addition, subtraction, and multiplication work with integers?
3. What is the **absolute value** of an integer, and how is it useful?
4. How do we solve integer-based equations (e.g., Diophantine equations)?
5. What is the **greatest common divisor (GCD)** of two integers?

**Tip:** Always remember, zero is an integer, and it plays a crucial role in various mathematical concepts.

Explore the world of integers, including positive, negative numbers, and zero. Learn the key properties, such as closure under addition and multiplication, and understand why division isn't always closed. Ideal for students in Grades 5-7.

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