Integer is a fundamental concept in mathematics. It refers to a set of positive and negative whole numbers, including zero. In simple words, integers are numbers that can be expressed without any fractional or decimal component.

Integers are represented by the symbol 'Z' and can be written as Z = {...,-3,-2,-1,0,1,2,3,...}. They are used in various mathematical operations such as addition, subtraction, multiplication, and division.

Properties of integers:

- Closure property: When two integers are added, subtracted, multiplied, or divided, the result will always be an integer.
- Commutative property: The order of the integers does not affect the result of addition and multiplication operations.
- Associative property: The way the integers are grouped in an addition or multiplication does not affect the result.
- Identity property: The sum of any integer and zero is the integer itself, and the product of any integer and one is the integer itself.
- Inverse property: Every integer has an opposite or additive inverse, which is obtained by changing the sign of the integer.
- Distributive property: The multiplication of an integer by a sum or difference of integers can be distributed over the integers.

Conclusion:

Integers are an essential part of mathematics, and their understanding is crucial in solving various mathematical problems. They are used in various real-life applications such as measuring temperature, distance, and time. Understanding the properties of integers can help in simplifying complex mathematical operations.

Integers is the set of numbers which contain negative numbers , zero and positive numbers.