Author: David_Corfield Format: HtmlFound some exposition by Todd on the web to add to <a href="http://ncatlab.org/nlab/show/ultrafilter">ultrafilter</a>, and a quote by Michal Barr added at <a href="http://ncatlab.org/nlab/show/ultraproduct">ultraproduct</a>.
This was prompted by a <a href="http://terrytao.wordpress.com/2010/01/30/the-ultralimit-argument-and-quantitative-algebraic-geometry/">comment</a> by Terry Tao
>There are two main facts that makes ultralimit analysis powerful. The first is that one can take ultralimits of arbitrary sequences of objects, as opposed to more traditional tools such as metric completions, which only allow one to take limits of Cauchy sequences of objects.
So are ultralimits in his sense a form of completion?
Found some exposition by Todd on the web to add to ultrafilter, and a quote by Michal Barr added at ultraproduct.
>There are two main facts that makes ultralimit analysis powerful. The first is that one can take ultralimits of arbitrary sequences of objects, as opposed to more traditional tools such as metric completions, which only allow one to take limits of Cauchy sequences of objects.
So are ultralimits in his sense a form of completion?