Di Nasso, Mauro; Zhang, Yi Nonstandard analysis and an application to the symmetric group on natural numbers. (English) Zbl 1020.03064 Zhang, Yi (ed.), Logic and algebra. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 302, 249-258 (2002). Summary: An introduction of nonstandard analysis in purely algebraic terms is presented. As an application, we give a nonstandard proof of a characterization theorem for compact subsets of \(\text{Sym} (\mathbb{N})\).For the entire collection see [Zbl 0994.00017]. MSC: 03H05 Nonstandard models in mathematics 20B30 Symmetric groups Keywords:compact subset of \(\text{Sym}(\mathbb{N})\); nonstandard analysis PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{Y. Zhang}, Contemp. Math. 302, 249--258 (2002; Zbl 1020.03064)