All things ultra

I’ve personally always been fascinated by the notion of an ultraproduct. Before I came to know of the construction, I guess it could’ve been because it kept popping up and was “unknown territory” – and the cool sounding name, I must admit. However, after actually knowing what the construction is all about, it doesn’t fascinate me any less, which is largely due to its powerful applications. I’ll here try to define the notion of ultrafilters, ultraproducts and ultrapowers as well as showing a particular application, namely a rigorous account of infinitesimals in a branch of mathematics called non-standard analysis. Continue reading