Arithmetic of Whole Numbers


Thousands of years ago, man began to represent numbers by the use of number symbols. Primitive man kept a record of a number by making scratches on a stone or in the dirt, by cutting notches in a stick, or by tying knots in a rope. He also kept a count of his animals by placing in a pile one pebble for each animal.

In each of these methods of recording numbers one mark stood for one object and there were as many marks as there were objects. In those early days of recording numbers, there was no one mark to stand for several objects.

After many years, man learned to represent several objects by using a single symbol. This was a great step forward in the development of number symbols.

Different peoples in ancient civilizations created number sybols of various kinds. Zero, the empty set, or something to hold a place came along much later.  When I play Sudoku I realize that Zero was a hard concept for the Asian to understand for a long time. Kakuro is another game of numbers that does not use Zero.

The number symbol or number name that is used to represent a number is called a numeral.

We must be aware of the fact that a numeral and the number it represents are not the same thing. The numeral is only the symbol for the number, not the number itself. we know for example that the number 4 is larger than the number 3 even though we might see a larger printed 3 and a small printed 4.

In our mathematics work we shall add, subtract, multiply and divide numbers, not numerals. At times however to avoid awkward and cumbersome language expressions we will use the word number when we should really use the word numeral. For example, we may say “write the number” instead of saying “write the numberal that represents the number.” This is commonly accepted practice.


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