Talk:Arctangent Logarithmic Formulation

Good as a first stab, but notice needs to be made of the fact that arctan is a multifunction. I call attention to Definition:Arctangent, for instance. Similar applies to other inverse trig functions. --prime mover (talk) 06:57, 14 December 2012 (UTC)


 * The logarithm is also a multifunction; as it happens, the identity holds as an equality of multifunctions. I have the impression though that insufficient caution with the peculiarities of complex logarithm is taken... It really cannot be well-defined on all of $\C$. --Lord_Farin (talk) 12:01, 14 December 2012 (UTC)


 * Are we using arctan to mean inverse tan now? --GFauxPas (talk) 14:33, 14 December 2012 (UTC)


 * We ought to. $\tan^{-1}$, as has been pointed out on the Tangent page, is misleading notation. arctan is de rigueur. --prime mover (talk) 14:42, 14 December 2012 (UTC)


 * Having said that, $\tan^{-1} (x)$ is a set: $\{y \in \C: \tan y = x\}$ which is well-defined. It's more complicated than it looks on the surface, and is tractable, but requires considerable fundamental underpinning. --prime mover (talk) 14:47, 14 December 2012 (UTC)


 * If we're using $y = \tan^{-1} x$ to mean $(x,y) \in \tan$, I object to using "$\iff$". (Actually, I object to even using $"="$, but that's a losing battle) --GFauxPas (talk) 14:53, 14 December 2012 (UTC)

I changed it to $ \arctan x $ (and the others too). — Timwi (talk) 19:33, 14 December 2012 (UTC)


 * I'm actually unhappy about the entire page until we have covered the multifunctional nature of logarithm in the complex plane. These grade-school definitions are all very well but they are a bit limiting and need to be expanded. This is one reason why this area has not been done; I was nerving myself up to posting up the fundamentals but got bogged down in the topology which I failed at badly. --prime mover (talk) 19:42, 14 December 2012 (UTC)