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Mathematics-Online course: Basic Mathematics - Natural Numbers

Properties of natural numbers

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The natural numbers

$\displaystyle \mathbb{N} = \{1,2,\ldots\}

can be characterized by the following axioms, due to Giuseppe Peano, an Italian mathematician:

The notation $ \mathbb{N}_0 = \mathbb{N} \cup \{0\}$ 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 $ 1$ by 0 .

(Authors: Höllig/Kimmerle/Abele)

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  automatically generated 10/31/2008