In fact I've been puzzled by this for a long time: the tag "differential-equations" is a tag about NDSolve, the tag "numerical-integration" is also a tag about NDSolve, isn't it overlaped? And, why does a tag about integration involve in NDSolve?

@xzczd NIntegrate?

@xzczd because "integration" has always been used to refer to integrating functions and differential equations?

@xzczd and no, differential-equations is about both DSolve[] and NDSolve[]. One symbolic, one numeric.

Limit[n^-n (BernoulliB[1 + n, n]/n), n -> Infinity]

Mma is so dumb sometimes

@Verde Mathematica has always been dumb; there are a lot of things it doesn't know, and what it does know can only be gleaned if you give it very specific instructions...

@J.M. oh ... I thought I was alone. Just complaining about my dumbness

@J.M. yeah, I know, I'm just thinking about if these two tags are partly overlapped, and I think the relation between integration and differential equation solving isn't so clear, maybe some edit should be done?

@xzczd Let's see, one says "for questions about DSolve[] and NDSolve[]", while the other says "for questions about NIntegrate[] and NDSolve[]". What's not clear?

Something completely random: guess what the following routine does.

fun[data_?MatrixQ, opts___] := Through[{Most, Last}[
   NArgMin[Norm[(Norm[{\[FormalH], \[FormalK]} - #] - \[FormalR]) & /@
       data], {\[FormalH], \[FormalK], \[FormalR]}, opts]]]

@J.M. so they're both about NDSolve[], what's the difference between them in this respect? Why not give them a clear division? And…I admit my English is poor… by saying "the relation between integration and differential equation solving isn't so clear", I want to express that though Differentiation and integration have close relations, they can still appear alone, especially in numeric calculation…maybe the tag can be changed into numerical-calculus?

@xzczd Basically, if you have both tags, then you're delineating that it's NDSolve[] that you're asking about...

！！！Hahaha, OK, that's a good reason.

Hmm, no one around, so...

@J.M. Code, or it didn't happen.

@J.M. How bad was the earthquake in Manila?

Hi Brett

@R.M Hello. So you're coming to the conference?

@BrettChampion no, I won't be coming this year

@R.M Too bad. :-(

Yeah :( Oh well, I'll make it there next year (most probably)

@Verde OMG...I'm so dumb...

@Verde Until some minutes later, I couldn't agree that f[x+a]:=x² could be expressed like (x+a)².

For the shifts we talked about.

ha, I just found a string for which google returns no results:

"EJB 352717-001"

@R.M Surprisingly enough, we never felt anything...

@BrettChampion Oh, alright; code for Truchet tiles isn't that long...

cell = With[{bsopts =
    Sequence[SplineDegree -> 2, SplineKnots -> {0, 0, 0, 1, 1, 1},
     SplineWeights -> {1, 1/Sqrt[2], 1}]}, {CapForm[None],
   Tube[BSplineCurve[#, bsopts],
      1/8] & /@ {{{0, 1/2, 1/2}, {1/2, 1/2, 1/2}, {1/2, 0,
       1/2}}, {{1/2, 1/2, 1}, {1/2, 1/2, 1/2}, {1/2, 1, 1/2}}, {{1/2,
       1/2, 0}, {1/2, 1/2, 1/2}, {1, 1/2, 1/2}}}}]

With[{n = 5},
 Graphics3D[
  Table[Translate[
    Nest[Rotate[#, RandomChoice[Range[0, 3] Pi/2],
       RandomChoice[IdentityMatrix[3]], {1, 1, 1}/2] &, cell, 2], {i,
     j, k}], {i, 0, n - 1}, {j, 0, n - 1}, {k, 0, n - 1}]]]

(I omitted the bit with SeedRandom[], though. >:))

@J.M. Re: your tag edits. I think derivatives deserve a tag on their own

@J.M. you seem to enjoy this sort of thing so maybe you know: if I have N unitary matrices $m_i$ and form $M_n=m_n.m_{n+1}\ldots m_{N-1}.m_1\ldots m_{n-1}$, then the eigenvalues of $M_n$ do not depend on $n$ but the eigenvectors do. that is, the eigenvalues of $M_n$ are independent of $n$ but the eigenvectors are not. I can show this by brute force, but I am wondering if there is some direct way to see it (there probably is, but I am not good at this sort of thing so usually go for brute force).

(or anybody else who can spot anything)

(and I guess they don't have to be hermitean actually, or so follows from my demonstration and playing with numerical matrices)

@R.M not sure if comments on deleted posts come through, so yes, will delete that post. It got a downvote anyway.

@Verbeia Thanks :) Took me a while to find a few unvisited ones... :P