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Mathematics-Online course: Basic Mathematics - Natural Numbers | ||

## Properties of natural numbers |

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The natural numbers

- For every natural number there is a successor.
- is the smallest natural number.
- Every subset of the set of natural numbers contains a smallest element.
- There are only finitely many natural numbers between any two natural numbers.
- By counting (starting with ), one passes through all natural numbers.

The notation is used for the set containing all natural numbers and 0.

Sometimes 0 is referred to as a natural number as well. In this case, the above properties remain valid by replacing by 0 .

(Authors: Höllig/Kimmerle/Abele)

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automatically generated 10/31/2008 |