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If a hyperreal <math>u</math> is represented by a Cauchy sequence <math>\langle u_n:n\in\mathbb{N} \rangle</math> in the [[ultrapower]] construction, then
:<math>\text{st}(u)=\lim_{n\to\infty}u_n.</math>
More generally, each finite <math>u\in{}^{\ast}\mathbb{R}</math> defines a [[Dedekind cut]] on the subset <math>\mathbb{R}\subset{}^{\ast}\mathbb{R}</math> (via the total order on <math>{}^{\ast}\mathbb{R}</math>) and the corresponding real number is the standard part of ''u''.
==Not internal==
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