Closure property means
if you apply the fundamental operations on integer / fraction / whole number you will get integer/ fraction/whole number

**Closure Property**

The closure property is a fundamental property in mathematics that applies to various operations, including addition and subtraction. It states that when performing an operation on two elements of a set, the result will also be an element of the same set.

In simpler terms, if we have a set and perform an operation (e.g., addition or subtraction) on any two elements from that set, the result will always be within the same set. This property ensures that the operation remains valid and consistent within the given set.

**Closure Property of Integers under Addition**

Integers are whole numbers, including positive, negative, and zero values. When we talk about the closure property of integers under addition, it means that when we add any two integers, the result will always be an integer.

For example:
- Adding two positive integers: 3 + 4 = 7
- Adding a positive and a negative integer: 3 + (-4) = -1
- Adding two negative integers: (-3) + (-4) = -7
- Adding an integer and zero: 3 + 0 = 3

In each case, the sum of the integers is still an integer, satisfying the closure property.

**Closure Property of Integers under Subtraction**

Similarly, the closure property of integers under subtraction means that when we subtract any two integers, the result will always be an integer.

For example:
- Subtracting a positive integer from a positive integer: 7 - 4 = 3
- Subtracting a negative integer from a positive integer: 7 - (-4) = 11
- Subtracting a positive integer from a negative integer: (-7) - 4 = -11
- Subtracting a negative integer from a negative integer: (-7) - (-4) = -3

In each case, the difference between the integers is still an integer, satisfying the closure property.

**Importance of Closure Property**

The closure property is essential in mathematics as it ensures that the results of operations remain within the same set. This property allows us to perform calculations and manipulate numbers while maintaining consistency and validity. Without closure, operations would not be well-defined, and mathematical systems would become unreliable.

Understanding and applying the closure property of integers under addition and subtraction is crucial when working with integers. It allows us to confidently perform calculations, solve equations, and explore various mathematical concepts involving integers.