**Whole Numbers:**

Whole numbers are a set of numbers that include all the natural numbers (positive integers) along with zero. In other words, whole numbers are non-negative integers that do not have any fractional or decimal parts. The set of whole numbers is denoted by the symbol "W" or "ℤ⁺⁰".

**Properties of Whole Numbers:**

1. **Closure Property:** The sum, difference, and product of any two whole numbers is always a whole number. For example, if we add or multiply any two whole numbers, the result will also be a whole number.

2. **Associative Property:** The associative property holds for addition and multiplication of whole numbers. This means that when adding or multiplying three or more whole numbers, the grouping of the numbers does not affect the result. For example, (2 + 3) + 4 = 2 + (3 + 4) and (2 × 3) × 4 = 2 × (3 × 4).

3. **Commutative Property:** The commutative property holds for addition and multiplication of whole numbers. This means that the order in which the numbers are added or multiplied does not affect the result. For example, 2 + 3 = 3 + 2 and 2 × 3 = 3 × 2.

4. **Identity Property:** The whole number zero (0) acts as the identity element for addition. When zero is added to any whole number, the result is the same whole number. For example, 5 + 0 = 5. However, zero does not have an identity element for multiplication. When zero is multiplied by any whole number, the result is always zero.

5. **Distributive Property:** The distributive property holds for the multiplication of whole numbers over addition. This property states that the product of a whole number and the sum of two other whole numbers is equal to the sum of the products of the whole number with each of the two other whole numbers. For example, 2 × (3 + 4) = (2 × 3) + (2 × 4).

6. **Closure under Subtraction:** Whole numbers are not closed under subtraction. This means that subtracting a larger whole number from a smaller whole number may result in a non-whole number, such as a negative number.

7. **Closure under Division:** Whole numbers are not closed under division. This means that dividing a whole number by another whole number may result in a non-whole number, such as a fraction or decimal.

Overall, whole numbers possess several important properties that allow for various arithmetic operations and calculations to be performed accurately. These properties make whole numbers a fundamental concept in mathematics and provide a foundation for further mathematical learning.

The collection of all natural numbers and 0 , are called WHOLE NUMBERS.
Other definition is: Numbers start from 0 and goes to infinity.