Does the Archimedean property apply to complex numbers?

Although the Complex numbers have no natural order, they have a norm or magnitude that satisfies the Archimedean Property. read more

Although the Complex numbers have no natural order, they have a norm or magnitude that satisfies the Archimedean Property. In this case, for all [math]0\neq z\in\mathbb C[/math], there exists an [math]n\in\mathbb N[/math] such that [math]|nz|>1[/math]. read more

This is a property of the real number field. It can be shown that any Archimedean ordered complete fields is isomorphic to the reals. In an ordered field in which the Archimedean property does not apply, there are numbers $\epsilon > 0$ so that $n\epsilon$ will not eventually exceed every element in the field. These are the so-called infinitesimals. read more

Archimedean property of the real numbers The field of the rational numbers can be assigned one of a number of absolute value functions, including the trivial function | | =, when ≠, the more usual | | =, and the p-adic absolute value functions. read more