# Talk:Complex Integration by Substitution

The house style suggests that the fraktur font should not be used. Thus, I've used $\operatorname{Re}$ and $\operatorname{Im}$ instead of $\Re$ and $\Im$ for real and imaginary parts in all my other pages. It's true that this leads to overloading of $\operatorname{Im}$, but it does not lead to ambiguity, as the image operator is used on a mapping or a set, while the imaginary part operator is always used on a complex n If people still doesn't like that we use $\operatorname{Im}$ for two different things in this theorem, I would much rather that we find another name for $\operatorname{Im} (\gamma)$, otherwise we would have to change all instances of $\operatorname{Im}$ for imaginary parts on other pages for consistency. --Anghel (talk) 20:37, 15 December 2012 (UTC)
Tricky. In this case I think the way you did it is the right thing. I hate to say, but we might need to go back to using $\Re$ and $\Im$ for Real and Imaginary after all. My hatred of fraktur notwithstanding (dates back from nightmare memories of failed attempts to teach me pre-war German), as the latter symbols seem to be not only $\LaTeX$-standard but also relatively unambiguous, it does make sense. --prime mover (talk) 21:53, 15 December 2012 (UTC)
Well, it was actually Timwi who "did it", as he changed my $\operatorname{Im}$'s to $\Im$'s. My main reason for disliking $\Im$ is that you can't write it on a blackboard (well, maybe somebody can, not not me). My tentative suggestion is that we denote images of sets with ordinary letters instead, and explain what they are, whenever we write about complex analysis. Then, we can still use $\operatorname{Re}$ and $\operatorname{Im}$ for real and imaginary parts. --Anghel (talk) 22:27, 15 December 2012 (UTC)
Example: "Let $f: A \to \C$" be a continuous complex function, where $A$ denotes the image of $\phi$" could be used on this page. I think this is the only page that both adresses images and imaginary parts. --Anghel (talk) 13:41, 16 December 2012 (UTC)
For my 2 cents, I consider overloading the best option. Perhaps distinguish $\operatorname{im}$ for image and $\operatorname{Im}$ for imaginary part (arbitrary, I know, but this is how I do it in practice; not that I need the former - in fact, either - very often). --Lord_Farin (talk) 22:39, 15 December 2012 (UTC)
There are more pages on this wiki that uses $\operatorname{Im}$ for images that for imaginary parts, so it would be time-consuming to implement your notation. If we change anything, it should be the imaginary part notation; but as I mentioned above, this page is the only page that talks about both images and imaginary parts. I believe overloading $\operatorname{Im}$ in ProofWiki notation would be okay. --Anghel (talk) 13:41, 16 December 2012 (UTC)