Definition talk:Canonical Variable

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The notation for variables in this as well as connected articles are more or less consistent and is chosen in such a way to save space in case of a proof. Traditional enumeration -first and last variable- takes too much space. This notation is clear, but a more elegant way of dealing with this should exist. One possibility was to introduce an ordered set of variables. However I am not sure how to properly implement this. Also, checking different sources of literature for notation could be problematic if notation used there has a context which differs from source to source. I am open to any suggestions, maybe there could exist two different sets of notations, one for definitions and the other for proofs. However, at the moment I do not know how to improve the situation without harming presentation of densely packed mathematical symbols. Julius (talk) 07:04, 30 January 2017 (EST)

"Traditional enumeration -first and last variable- takes too much space." No more space than three dots, element, three dots. But that is not the point. A far better technique would be to use vector notation, as that's what that ugly object effectively is.
We are (or we intend to be) rigorously consistent in all our notation, for reasons which we had always considered to be self-evident. It takes time and effort to craft the pages into the form that makes them adhere to our house style, and it can be tedious going through and changing it once there is a vast quantity of material to be tidied up. But then, it's easy just to copy pages from a cheap Dover textbook -- the value added by our website is a presentation of proofs and definitions to an exacting standard of aesthetic quality. --prime mover (talk) 09:07, 30 January 2017 (EST)
"No more space than three dots, element, three dots" is true assuming that there is no summation across all members, and that only one such set of variable exists. Once that is taken into account, we have "three dots, i-th component, three dots" over "first variable, three dots, i-th variable, three dots, last variable" multiplied by number of such sets of variables per function, and the difference in space usage is evident.
I am not sure that vector notation should be used here. I do not know if dependence on a vector implies dependence on a whole object rather that its components, or both interpretations are possible. In that case I would use vector notation. But this has to be clearly stated, and "effectively" does not cut it. Either it is a vector or it is not. Until then, I am hesitant to include a notation which would require additional explanation while not necessarily being rigorous or final. If there was a strict house rule or a page with definitions or explanations, I would follow it by the letter.
Copying is indeed easy. That is why it is the first step in knowledge acquisition. As children copy their parents, students copy lecturers' notes and scientists copy methods of other scientists to make the first step, in the same way the first step has to be done when including material on this website. In addition to this, here it was encouraged to contribute by adding more material. I understand the goal of this website, but if are lacking even some basic undergraduate material, trying to enforce perfect form from the first moment the given article appears seems to be mismanagement of resources. After all, 80/20 rule should be working to some extent.
It is tedious to go over all articles again and again, but that is to be expected, so that cannot be an excuse. Everybody, who starts an article and leaves it unfinished and then moves to a different literature source should be encouraged to get back and clear up all the leftovers. I know that and I am planning to revisit them again and again. Also, from the most recent changes it seems that more time is being spent on new definitions rather than the mend of articles in "to do" section. If consistent notation was the ultimate goal, changes in the "to do" list of pages would appear daily. However, that is not the case, and of course the mood is set accordingly. Julius (talk) 11:47, 30 January 2017 (EST)
The trouble is though it's going to be muggins who ends up cleaning up this colossal heap of ugly code. --prime mover (talk) 13:31, 30 January 2017 (EST)
Somebody will, but let's not rush with conclusions. A little patience can go a long way (which, realistically, may need several months for completion). I consider digging through a complete heap much more interesting rather than an incomplete one. And if there is joy, time is not a factor anymore. Julius (talk) 14:13, 30 January 2017 (EST)