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An Introduction to Mathematical Reasoning by Peter J. Eccles

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13

Number systems

Numbers originally arose for the purpose of counting. This makes use of the positive integers images often called the natural or counting numbers. In order to write down numbers we need some system of numerals, a system of symbols to represent numbers. At first the notation used was simply some sort of tally or repeated mark but in time more elaborate systems of numerals were devised leading eventually to our present Hindu-Arabic decimal system of numerals which makes use of ‘cypherization’ (i.e. different symbols 1, 2, 3, 4, 5, 6, 7, 8, 9 for different numbers) and a ‘place value system’ (e.g. in 121 the first ‘1’ denotes 100, the ...

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