Z represents the set of all integers. This encompasses all whole numbers (both positive and negative) including zero.
Understanding Integers (Z)
The set of integers, often denoted by the symbol Z, consists of:
- All positive whole numbers: 1, 2, 3, 4, ...
- All negative whole numbers: -1, -2, -3, -4, ...
- Zero: 0
Therefore, Z = {..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}.
Why "Z"?
The notation "Z" comes from the German word "Zahlen," which means "numbers."
Key Properties of Integers
- Closure under addition, subtraction, and multiplication: Adding, subtracting, or multiplying any two integers always results in another integer.
- Not closed under division: Dividing two integers does not always result in an integer (e.g., 3 / 2 = 1.5, which is not an integer).
- Ordered set: Integers can be arranged in a specific order from least to greatest.
Examples
Here are a few examples illustrating how integers are used:
- Temperature: A temperature of -5 degrees Celsius represents an integer value.
- Bank Balance: A bank balance of $0 or -$50 (representing an overdraft) are integer values.
- Counting: Counting objects (1 apple, 2 apples, etc.) results in integer values.
- Altitude: Describing a height above or below sea level (e.g., 100 meters above sea level or -20 meters below sea level).
