Natural numbers are the numbers 1,2,3… which are used for counting. Successor of a natural number is obtained by adding 1 to it. Predecessor of a natural number is obtained by subtracting 1 to it. Every natural number has a successor. Every natural number except 1 has a predecessor.
The natural numbers along with zero is called the collection of whole numbers. Every whole number has a successor. Every whole number except zero has predecessor.
All natural numbers are whole numbers, but all whole numbers are not natural numbers.
Whole numbers can be represented on a number line by marking the numbers using the fixed distance between them. The distance between 0 and 1 is called unit distance. Other points are marked to the right of 1 at unit distances from the previous point.
To add whole numbers on the number line, points to the right hand side of the numbers are counted. To subtract whole numbers on the number line, points to the left hand side of the numbers are counted.
Multiplication corresponds to making jumps of equal distance starting from zero. Division by zero is not defined.
Properties of whole numbers:
Closure Property: Whole numbers are closed under addition and multiplication. Whole numbers are not closed under subtraction and division.
Commutative Property: The addition and multiplication are commutative for whole numbers. Subtraction and division are not commutative for whole numbers.
Associative Property: Associativity of addition and multiplication are applicable to whole numbers. This property is not true for subtraction and division.
Distributivity of multiplication over addition: Distributivity of multiplication over addition are applicable to whole numbers.
Additive and multiplicative identity for whole numbers: Zero is called an identity for addition of whole numbers or additive identity for whole numbers. 1 is the identity for multiplication of whole numbers or multiplicative identity for whole numbers.
Patterns with numbers are helpful in understanding properties of numbers better. Whole numbers can be arranged in elementary shapes, like line, square, rectangle and triangle, made up of dots.