= Natural number
{title2=$\mathbb N$}
{wiki}
= Nonnegative integer
{synonym}
= Non-negative integer
{synonym}
The <natural numbers> are the nonnegative <integers>
$$
\mathbb N=\{0,1,2,3,\ldots\}.
$$
They count the elements of <finite sets>: the <empty set> has <cardinality> zero, and a two-element <set> has <cardinality> two. <Addition> and <multiplication> preserve <natural numbers>, while <subtraction> need not: $2-3=-1$ is an <integer> outside $\mathbb N$.
The convention here includes zero. The <positive integers> instead begin at one. The <well-ordering principle for the natural numbers> ensures every nonempty <subset> has a least element, supporting <mathematical induction> and <proof by minimal counterexample>.
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