Talk:Division Theorem
Hey, take a look at this page, Division Algorithm! Should we merge, or delete that one and create a redirect, I've not compared both, but it seems like there done differently, so I suggest merger. --Joe 22:57, 11 October 2008 (UTC)
I don't know, that one seems less rigorous somehow. I can't find a specific problem, though. If we do merge them, make sure we standardize them first, since this one uses $a=qb+r$ and that one uses $b=aq+r$. --cynic 23:52, 11 October 2008 (UTC)
Although not as rigorous, it's still valid (I hope). If I get a chance later this evening I'll merge them. Which title should we stick with for the main title
- Division Theorem
- Division Algorithm
I know both are fairly popular. --Joe 01:19, 12 October 2008 (UTC)
wikipedia uses division algorithm, and i can't find an article on wolfram for either (weird, but whatever). Doesn't matter which we use, just make sure that the other one links to it. --cynic 03:39, 12 October 2008 (UTC)
Oo-er, sorry ... never realised this was already up. I did look, honest, just not hard enough ...
Suggest that the version in "Division Algorithm" be moved as an "alternative proof" into the "division theorem" version and the "division algorithm" page left, not as a bald redirect, but with a few words and with a link. There are reasons to consider "division algorithm" as a less good title, as it gets confused with the Euclidean Algorithm (still to be posted, I believe). --prime mover (talk) 05:31, 12 October 2008 (UTC)
- Just wandering through the stubs...wouldn't the generalisation to $\R$ be $\forall a,b\in\R \exists c\in\R : a=bc$?
- At least I thought of this as "approximation to division for integers", so for a field we have the stronger result $r$ can always be taken to be zero. --Linus44 10:45, 7 March 2011 (CST)
- I think I may have been thinking along the lines of the generalization of modulo arithmetic to real numbers at the time. Looking at it now I believe I wasn't thinking sensibly. --prime mover 13:37, 7 March 2011 (CST)