7:45 AM
2

A new tag piecewise-continuity has been created by a new user. Currently the tag is used by only 7 questions - all written by the tag creator. All this is typical of a well-meaning user who is not experienced enough about either math in general, or tagging on our site in particular, or both. My...

1 hour later…
8:46 AM
in Floor function and other jump discontinuous functions, 30 secs ago, by Martin Sleziak
@TheGreatDuck I just wanted to let you know that the tag (and possibility of its removal) is discussed on meta: http://meta.math.stackexchange.com/questions/22348/tag-management-2016/23571#235‌​71
I thought it is a good idea to ping the (probable) tag-creator.

9:12 AM
Thanks @Martin. FWIW the system flagged the creator's string of edits (just adding this tag) as possible vandalism. That was certainly a wrong diagnosis, because we can safely exclude the possibility of any malicious intent. Yet such a system flag may affect my attitude. Also, if I had the power I would completely forbid the creation of new tags without discussing them here (or the annual predecessors/successors of this thread). And that should apply to veterans and newbies alike. — Jyrki Lahtonen ♦ 16 mins ago
This was previously discussed on meta:
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In several discussions here on meta, one user expressed the opinion, that every new tag (or at least most of them) should be discussed on meta before creating. For example here There is a saying that it's easier to apologize later than get permission first. I disagree with that when it comes...

11 hours later…
8:18 PM
@MartinSleziak since it is still being discussed I will post questions that I find to fall under the tag here. I'm not picking arbitrarily. Yes, I am just searching piecewise but I am reading the questions first. I just figured it was an easy way to find relevant topics. Some even ask about piecewise continuity itself (not just piecewise continuous graphs).
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I'm a little bit confused in piecewise continuity of a function. Say, if we have an odd function like $f(x) = x$ defined on the open interval $(0, \pi)$. We then extend it to a period $2\pi$ function and find its sine Fourier series. Can we say that this function is then piecewise continuous, but...

2

if I have a piecewise continuously differentiable function. How do I see that on each open interval, where the derivative is continuous, there is a continous extension on the larger closed interval?

1

Assume $f$ and $g$ are two piecewise continuous functions on an interval $( a , b )$ containing the point $t_0$ . Assume further that $f$ has a jump discontinuity at $t_0$ while $g$ is continuous at $t_0$ .How can i verify that the jump in the product $fg$ at $t_0$ is given by “the jump in $f$ at...

1

Say we have the piecewise function $f(x) = x^2$ on the interval $0 \le x < 4$; and it equals $x+1$ on the interval $x \ge 4$. Why is it that, when I take the derivative, the intervals loose their equality and become strictly greater or strictly less than?

0

Let be $f:\mathbb{R} \rightarrow \mathbb{C}$. Consider the space of piecewise linear curves, with support in the interval [-1,1], sucht that $f(x)= A-|x|$ if $|x|\leq 1$; $f(x)= 0$ otherwise. For this space show that expression $p(f)=\int_{-\infty}^{\infty}|f(x)|^2dx$ is a norm. I am show that \$...

Just to add even more potential sources
i narrowed the field a bit
I obviously did not read every single question in the search
but 23 pages of "piecewise continuous" as a search definitely seems to imply a decently sized chunk
That is roughly 1125 sources to pull from
assyming a 1/2 amount that actually qualify
that is 550 questions that qualify
and they do help sort meaning. Piecewise continuous functions are a pretty major subset
en.m.wikipedia.org/wiki/Piecewise The Wikipedia page definitely indicates it isn't just a random useless subject
Floor function, absolute value, piecewise notation, most indicator functions, modulo...
all of them are piecewise continuous
Anyway, that's what I found supporting its existence at the moment
im sure it is weak evidence
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.