Definition:Archimedean Property

Definition
Let $\struct {S, \circ}$ be a closed algebraic structure on which there exists either an ordering or a norm.

Let $\cdot: \Z_{>0} \times S \to S$ be the operation defined as:
 * $m \cdot a = \begin{cases}

a & : m = 1 \\ a \circ \paren {\paren {m - 1} \cdot a} & : m > 1 \end {cases}$

Also see

 * Definition:Infinitesimal