For question about natural numbers $\Bbb N$, their properties and applications

In mathematics, the natural numbers are those used for counting ("there are six coins on the table") and ordering ("this is the third largest city in the country"). These purposes are related to the linguistic notions of cardinals and ordinals, respectively (see English numerals). A later notion is that of a nominal number, which is used only for naming.

Properties of the natural numbers related to divisibility, such as the distribution of prime-numbers, are studied in number-theory. Problems concerning counting and ordering, such as partition enumeration, are studied in combinatorics.