Parodi

Hello, Parodi, and Welcome to Wikipedia! Please remember to sign your name on talk pages by clicking or or by typing four tildes (~~~~); this will automatically produce your username and the date. Also, please do your best to always fill in the edit summary field. Below are some useful links to facilitate your involvement. Happy editing! Fæ (talk) 12:10, 18 May 2010 (UTC) Getting started Introduction The five pillars of Wikipedia How to edit a page Intuitive guide to Wikipedia Finding your way around Table of contents Department directory Editing articles How to develop an article Manual of Style Getting help Frequently asked questions Cheatsheet Where to ask a question Help pages New contributors' help page Article Wizard - a Wizard to help you create articles How you can help Contributing to Wikipedia Community Portal Follow Wikipedia etiquette Practice civility

Vector valued function

I see that you added a mention of infinite dimensional vector-valued functions. That's completely beyond my expertise, but you seem to imply that the standard rules of differentiation for finite dimensional vector valued functions are not valid for infinite dimensions. Is it more complicated that just saying i goes from 1 to infinity instead of 1 to 3? MarcusMaximus (talk) 04:49, 2 July 2010 (UTC)

I now added an answer to the page. Roughly: if the number n of dimensions is finite (and we use the standard Euclidean topology), then the topology works nicely componentwise, i.e., you can compute derivatives and other limits componentwise. If n is infinite, then one usually uses a topology that is stronger, so that a limit need not exist even if a componentwise limit exists. However, you don't need these facts unless you are faced with an infinite-valued vector function, in which case you should first learn some basics of infinite-dimensional vector spaces, such as a Hilbert space. --Parodi (talk) 14:49, 1 October 2010 (UTC)