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	Mathematics-Online lexicon:
	Properties of 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 .

see also:

• Keyword: Peano
• Keyword: Numbers: natural numbers and integers