What Have We Discussed ?

1. The numbers 1,2,3,.....0,1,2,3,... which we use for counting are known as natural numbers.

2. Every natural number has a successorpredecessor. Every natural number except 1 has a predecessor.

3. If we add the number to the collection of natural numbers, we get the collection of whole numbers W = {0, 1, 2, ...}

4. Every whole number has a successorpredecessor. Every whole number except has a predecessor.

5. All numbers are whole numbers and all whole numbers except zero are natural numbers.

6. We can make a number line with whole numbers represented on it. We can easily perform the number operations of addition, subtraction and multiplication on such a number line.

7. Addition corresponds to moving to the rightleft on the number line, where as subtraction corresponds to moving to the leftright. Multiplication corresponds to making jumps of equal distance from .

8. Whole numbers are closed under additionsubtraction and multiplicationdivision. But whole numbers are not closed under subtraction and division.

9. Division by zero is not definedinfinity.

10. 0 is the additivemultiplicative identity and 1 is the multiplicativeadditiveidentity of whole numbers.

11. Addition and multiplication are commutativenot commutative for whole numbers.

12. Addition and multiplication are associativenot associative for whole numbers.

13. Multiplication is distributive over addition for whole numbers.

14. Commutativity, associativity and distributivity of whole numbers are useful in simplifying calculations and we often use them without being aware of them.

15. Pattern with numbers are not only interesting, but are useful especially for mental calculations. They help us to understand properties of numbers better.