Talk:Euler Formula for Sine Function

Refactor
I think it would be a good idea to split the theorem into 2 pages, one with proofs for real $x$ (like we currently have) and one with proofs for complex $z$ (the one I just added can be made to work for $z$). Is that a good idea? --Oliver (talk) 15:01, 11 May 2014 (UTC)


 * We had a long and inconclusive discussion on another page about how to attack a result which applies to both real and complex numbers. On the one hand, the same proof ought to do for both -- but on the other hand, we want to ensure that there is a "real analysis" thread running through the whole site so as to cater for students who have not encountered complex numbers. So what will basically happen is either that there will be "real" versions of a proof and a practically identical "complex" version, or a "one size fits all" version which talks about a result on a general field which may be either $\R$ or $\C$. My preference (despite the extra complexity) is for the first option (two separate proofs, with some words explaining this) despite the extra work involved.  This is based on the fact that continuity and limits are effectively defined differently between the two, unless you do it all in the language of metric spaces -- which then raises the issue of the fact that not all students will have been introduced to topology (the latter wasn't part of my undergraduate work -- it waited till my MMath before I got it formally).


 * TL;DR: yes, two proof threads: one for real, one for complex (and, as usual, a separate page for each individual proof). --prime mover (talk) 16:23, 11 May 2014 (UTC)