Properties of Integers:
Integers are whole numbers that can be positive, negative, or zero. They have certain unique properties that distinguish them from other types of numbers.

1. Closure Property:
Integers are closed under addition and subtraction. When two integers are added or subtracted, the result is always an integer.

2. Commutative Property:
The order of integers does not affect the result of addition or multiplication. For example, a + b = b + a and a * b = b * a.

3. Associative Property:
Integers follow the associative property for addition and multiplication. This means that (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c).

4. Identity Property:
The identity element for addition is 0, as adding 0 to any integer does not change its value. The identity element for multiplication is 1, as multiplying any integer by 1 gives the integer itself.

5. Inverse Property:
Every integer has an additive inverse, which is the negative of the integer. For example, the additive inverse of 5 is -5. However, not all integers have multiplicative inverses.

6. Distributive Property:
Integers follow the distributive property, which states that a * (b + c) = a * b + a * c. This property is useful in simplifying expressions involving integers.

7. Order Property:
Integers can be ordered from least to greatest or greatest to least. This property is useful in comparing integers and determining their relative positions on a number line.
These properties of integers make them a fundamental part of mathematics and play a crucial role in various mathematical operations and calculations.