Tagging - 2020-10-19

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5:19 AM

deleted-tag The tag inverse-trigonometry is now gone. math.stackexchange.com/posts/3870218/revisions

new-tag Two new tags resolvent and volterra-integral-equations were created by Karagum.

Q: Volterra equation $y(x)=\cos(x)-x-2+ \int_0^x(t-x)y(t)dt$

Solve the following Volterra integral equation: $$y(x)=\cos(x)-x-2+ \int_0^x(t-x)y(t)dt.$$ My attempt so far: By iterated kernel method we get \begin{align} K_n(x,t) &=\frac{(-1)^{n-1}}{(2n-1)!}(t-x)^{2n-1}, \qquad t\le x,\\\\ K_n(x,t) &=0, \qquad x\le t \end{align} Then it co...

2 hours later…

Martin Sleziak

7:08 AM

A good question! I don't want to go off on a tangent, but this is unfortunately not limited to this tag (number-theory and set-theory are often abused as well). I think we should encourage more users to read the tag wikis but idk how to do so... — Integrand 6 hours ago

@Integrand As discussed quite recently, a different between number-theory and set-theory is quite big - because there are user who carefully follow both set-theory and elementary-set-theory and if some questions are, they retag them. You can check who are the users who most frequently add or remove set-theory and which users ... — Martin Sleziak 3 mins ago

... often add and remove elementary-set-theory. (Removals are probably more relevant if we're looking at sets related to cleaning up tags.) — Martin Sleziak 2 mins ago

Corresponding stats for number-theory: adding and removing.

And for elementary-number-theory: adding and removing.

Another problem with these tags is that the discussion what actually should be content of these tags and whether elementary-number-theory should be a subset of number-theory was abandoned without reaching some clear consensus.

I will add some links to previous discussions of (elementary-number-theory) vs. (number-theory): How to differentiate between (elementary-number-theory) and (number-theory) and There are 5,931 questions tagged both elementary-number-theory and number-theory. (My impression is that the discussion about those tags wasn't really resolved - but at the moment we should stick with the usage described in the tag-infos.) — Martin Sleziak Sep 30 at 0:52

BTW the same thing was pointed out in that discussion:

"Why are questions tagged NT not being regularly retagged?" Fair question, I don't know. It could be that users don't distinguish between it and ENT; it could be that mass retagging is typically frowned upon, especially since it bumps questions. My guess is that many users don't read tag wikis or descriptions, or tag questions based on what's 'in' the question as opposed to what the question is 'about'. — Integrand Sep 30 at 15:27

It seems that the tag number-theory is not monitored as in (e.g.) set-theory. I find quite a lot of new questions not even related to number theory. — Arctic Char Sep 30 at 16:02

4 hours later…

Martin Sleziak

10:48 AM

new-tag A new tag symbol was created by Ongky Denny Wijaya - but we already have notation. I have edited the tags on this question: math.stackexchange.com/posts/3871795/revisions

Q: What the mean of $\mathbb{I}$ in equation (7)?

I try to understanding this paper. In equation (7), I don't know the symbol "$\mathbb{I}$" mean. What the "$\mathbb{I}$" mean? Is that identity matrix? In the paper is not explained what "$\mathbb{I}$" mean.

symbol

Q: What the mean of $\mathbb{I}$ in equation (7)?

functions notation

9 hours later…

Martin Sleziak

8:12 PM

new-tag A new tag equidecomposable was created by QED.

Q: Why these two sets have to be disjoint?

Consider the following relation between sets in $3$-dimensional Euclidean space. We say $$X\approx Y$$ if there is a finite decomposition of $X$ into disjoint sets $X=X_1\cup X_2\cup\cdots\cup X_m$ and a decomposition of $Y$ into same number of disjoint sets $Y=Y_1\cup Y_2\cup\cdots\cup Y_m$ such...