@TheGreatDuck I am not a native English speaker, but my impression is that the word opinionated has some negative connotations. I definitely do not think that the users who entered the discussion of this tag in the comments are in some way prejudiced.
@MartinSleziak there are a lot of questions. Piecewise notation questions (they are a big candidate as there is no tag for them), floor questions about jump discontinuity, etc. it appears there are a large number of them. It's just a matter of tagging them. See my recent edits for a few I found very easily be searching "piecewise". All of them count as candidates. — TheGreatDuck10 hours ago
@T.Bongers His complaint is assuming that the only taggable questions are mine. Im simply establishing that it is not true and that many questions could use the tag. — TheGreatDuck4 hours ago
Both from this comments and from what you wrote here in chat I get the impression that simply the fact that there are many questions about piecewise continuous question is a sufficient reason to create a tag.
That is not the case.
For example, there are plenty of questions concerning subgroups. Yet the tag subgroups was removed at least once and the discussion on meta suggests that experienced users are against creating this tag.
Tags, as I see them, have three major roles to play, under ideal settings:
They hint the reader what sort of topic the question will be, before opening it. Thus, using correct tags will help increasing the exposure of the question to its target audience.
They help partition the database into mo...
@MartinSleziak there are a lot of questions. Piecewise notation questions (they are a big candidate as there is no tag for them), floor questions about jump discontinuity, etc. it appears there are a large number of them. It's just a matter of tagging them. See my recent edits for a few I found very easily be searching "piecewise". All of them count as candidates. — TheGreatDuck11 hours ago
From the above comment, my impression is that maybe you intended to create a tag for piecewise defined functions (as opposed to piecewice continuous functions).
@TheGreatDuck You mentioned floor function and absolute value as examples. I hope you are not suggestoin that every question about them should also be tagged piecewice-continuous.
That would be definitely a bad idea. With this style of tagging we would soon run out of space - maximal number of tags which can be used on a question is 5 tags.
@MartinSleziak i did not intend to create a tag for piecewise defined functions. I meant to create a tag meaning piecewise continuous which is synonymous for piecewise continuous. No, I do not intend to place the tag on every single floor and absolute value question. However, I would intend to place it on one's that ask specifically about their discontinuity. Piecewise comtinuous functions actually make up the majority of functions.
in fact, I would argue that they are a braoder subject area than continuous functions
I simply mean that a lot of piecewise defined functions might fall into it
so it also fills that hole
Like in my list of examples, they all ask about piecewise comtinuity
I mean to say that there are more discontinuous functions than continuous functions, and the discontinuous one's we do study tend to be piecewise continuous.
but I think you'll agree it is worth taking a closer look at beyond just "discussing it in an opinionated fashion". I am clearly not the only one to ask these questions.
Clearly your opinion on the issue differs from the opinion from users who entered the debate so far. I think that it is good that some users expressed their opinions on the matter.
The comment I copied sounded like "opinionated discussion" was a bad thing.
But discussing tags is probably more relevant here than discussing word choice.
@TheGreatDuck: No. The main complaint is that you created this tag in the first place - without checking first here that experienced users find the tag helpful. I agree with T.Bongers that we don't need this tag. Mind you, I have seen worse suggestions for new tags, but that does not mean that I would approve of your tag, — Jyrki Lahtonen ♦47 mins ago
But as I have already mentioned, the number of questions is definitely not the most important criterion when judging whether a tag is useful. There are objectionable tags which have many questions and there are good tags containing only handful of questions.
Tags, as I see them, have three major roles to play, under ideal settings:
They hint the reader what sort of topic the question will be, before opening it. Thus, using correct tags will help increasing the exposure of the question to its target audience.
They help partition the database into mo...
If I'm doubtful about whether a new tag is appropriate, I apply the following tests:
Can I imagine at least two other users independently deciding that this tag is worth using or searching for? (This is a very weak test but any tag that it rejects should definitely not be used.)
Will any quest...
If the criterion for creating new tag would be "not covered by existing tags", then piecewise-continuous $\subseteq$ real-analysis (more-or-less, but definitely for the majority of cases where this type of functions occur.)
But real-analysis is a large area. If a new tag is suggested and it would be typically only used for questions from real analysis, this is not automatically a reasons against creating a tag.
well i think i can sum up a list of potential subjects that it covers (which are not covered in other tags quite well). This will probably help see if there are ways it helps index. Idk the exact distribution of questions. There is jump series (probably irrelevant), implied integration (probably irrelevant), polygonal curves, piecewise defined functions, indicator functions, jump discontinuity, etc.
Granted, indicator functions arent always piecewise continuous, so that is probably more of an issue for another day.
I definitely do not see questions about jump discontinuities as a good fit for the proposed tag. This is about a local behavior at the point of discontinuity.
We have periodic-functions which is more suitable for the last one you mentioned.
well piecewise continuous is synonymous with jump discontinuous
so id argue that they would fall under it, though every situation is different.
im merely talking about the most likely case for questions asking specifically about the continuity, not just whether there is discontinuity
@MartinSleziak jump discontinuity is the same thing. Its just a rebranding. You do know that right? Though I do like the sound of "jump discontinuity" better then "piecewise continuity".
You have mentioned piecewise defined functions and a while ago you said that your intention was not to create tag for piecewise defined functions, that there is a difference between piecewise defined and piecewise continuous.
@TheGreatDuck When I look at classification of discontinuities it seems to be a local thing. It is not difficult to imagine a function which have both jump discontinuity and essential discontinuity.
@TheGreatDuck Would you consider Thomea's function (a.k.a popcorn function) piecewise defined? It is definitely not piecewise continuous?
@TheGreatDuck I should leave, too.
The summary of the last few messages here in chat seems to be that we clearly disagree about the range of the question where piecewise-continuity would be applicable.
By the last comment I meant usage of continuity for questions about discontinuities/discontinuous functions.
The example with Thomae's function can be replaced by almost any function which is defined separately on $\mathbb Q$ and $\mathbb R\setminus\mathbb Q$.
The group of rational numbers $(\mathbb Q,+)$ has an interesting property , that the intersection of any two non-trivial subgroups of this group is non-trivial . Let us call this property the " non-trvial intersection property " or NIP in short . Now it is easy to see that this NIP property is i...
I already know that converse of Lagrange theorem does not hold on $A_n$.
If converse of Lagrange theorem does hold on $A_n$ , Some group of $A_n$ has all 3cycles and it is whole group.
Could you help me?
I have merged sub-groups into subgroups (which effectively just renamed the tag).
I am not personally convinced of the viability of even the correctly spelled tag. That's probably a topic for the other thread.
In this post I have suggested the synonym subgroups $\to$ group-theory. This synonym would prevent this tag from being created again as a standalone tag.
Other possibility could be to reconsider whether sugh tag might be in fact useful.
If I'm doubtful about whether a new tag is appropriate, I apply the following tests:
Can I imagine at least two other users independently deciding that this tag is worth using or searching for? (This is a very weak test but any tag that it rejects should definitely not be used.)
Will any quest...
I have merged sub-groups into subgroups (which effectively just renamed the tag).
I am not personally convinced of the viability of even the correctly spelled tag. That's probably a topic for the other thread.
