User talk:Robkahn131

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Cheers! prime mover (talk) 03:25, 31 March 2020 (EDT)

Sources section

Please take however long you need to explore how the "Sources" section works. --prime mover (talk) 18:19, 6 May 2020 (EDT)

I say to you again: please take note of the "Sources" section and see if you can work out how it is to be used. --prime mover (talk) 17:19, 7 May 2020 (EDT)

Sorry about that - I swear I'm not intentionally trying to irritate you. :) I copied a page over and forgot to delete the Sources section.

Some good posts, by the way, nice job. --prime mover (talk) 02:22, 8 May 2020 (EDT)
Thanks! I am really enjoying this creative outlet.

Proof numbering

One thing I'm puzzled about, that nobody has ever been able to answer, is this:

When people add new proofs, when there is already one or more proof in existence, they often make their new proof Proof 1, and rename / renumber all the other proofs as Proof 2, Proof 3, and so on.

I just wondered why they do this, rather than just add their new proof underneath the existing ones. Is there an inherent intrinsic natural ordering of proofs that makes it more "natural" for any given set of proofs to be ordered by? My personal view is that if there is such an ordering, then maybe we should order them in (at least approximate) chronological order of initial publication (if we have the patience to trawl through the literature to find it).

Thoughts? I ask, because this seems to be your own standard practice. --prime mover (talk) 06:34, 8 May 2020 (EDT)

There is a reason - Zeta of 4 had the Fourier analysis as proof 1, so I was trying to make zeta of 6 consistent with zeta of 4
Two additional thoughts:
1) For zeta of 2, 4, 6, etc, I would think there would be consistency in the proof ordering across these topics and
That seems to me like it would be a rod for your own back. But if that makes sense to you, knock yourself out.
IMO once we have a general method of proof for any arbitrarily large $n$ such that we effectively have a recipe for zeta of any even number, that is via the Bernoulli numbers, all the other proofs are merely curiosities.
I completely agree. However, for reasons that I can't explain, I like to see certain curiosities.
Curiosities are fun and I welcome their documentation. But IMO they don't get top billing. Or at least, they don't merit renumbering everything to put them at the top. Imo.
Having said that, if you want to assemble all the proofs of type X for zeta 2, zeta 4, zeta 6, etc. you could always do a page for "zeta of 2n by Fourier", etc. and transclude them all. --prime mover (talk) 15:08, 8 May 2020 (EDT)
2) Some proofs seem more satisfying to me. I realize that a proof is a proof, but I'd like to see the more satisfying ones up top.
"Satisfying"? - Different proofs put a different spotlight on the problem. But the problem of course is that what is satisfying to me may or may not be satisfying to others.
Indeed, in that final statement you are highly likely to be correct.
In this context, the "satisfying" proof is the one which covers the entire field in one go -- that is:Riemann Zeta Function at Even Integers. Then the elegant proof is the one which plugs the number into that. There's nothing more satisfying than polishing off something which is on the surface really complicated by means of a simple 3-liner: "here's one I made earlier, use that."
And indeed further: building a fourier series for ever more increasing n is all well and good, but it's a bit like the early days of integral calculus where whoever-it-was proved $\int x^n \rd x = \frac {x^{n + 1} } {n + 1}$ for bigger and bigger $n$ but never proved the general formula. All that hard work blown out of the water by Primitive of Power. And the technique where you equate coefficients of the Taylor series for sin x / x, again, well okay, but first you have to get those coefficients, which for larger $n$ is more and more tedious -- and even then the implementation on the proof page needs more than just handwaving, even a page like "coefficient of (whatever n) in the expansion of the Taylor series of sin x / x" or whatever -- again, not what I'd call elegant.
I agree again. It goes back to my own quirkiness on this one - I'm just curious to see what some of this minutae looks like.
Incidentally, you may wish to experiment with the technique of indenting replies to talk page posts, so as to make it clear what's a post and what's a reply. I have taken the liberty of adjusting your responses here accordingly. --prime mover (talk) 09:14, 8 May 2020 (EDT)
My ignorance will astound you!! :). I didn't know about the colon thing until I saw it here.
Separate topic - if one wanted to represent {I, -1, -I, 1} in a series, they could simply put I^k in the series to accomplish that. How does one do that for {sin(x), cos(x), -sin(x), -cos(x)}? The reason I ask - in Primitive of $x^n \cos a x$ all integrals can be removed and the result can be expressed as a power series. The pattern is obvious - the a in the denominator starts at 1 and moves up to (m+1), the x starts at m and goes down to 0. The coefficient is just a falling factorial.
$\frac {\sin a x} a x^6 + \frac {6 \cos a x} {a^2} x^5 - \frac {30 \sin a x} {a^3} x^4 - \frac {120 \cos a x} {a^4} x^3 + \frac {360 \sin a x} {a^5} x^2 + \frac {720 \cos a x} {a^6} x - \frac {720 \sin a x} {a^7}$
How about $\sequence {\dfrac {\d^n} {\d x^n} \sin x}_{n \mathop \in \N_{>0} }$?
How about $\displaystyle \sequence {\map {\sin} {x + \frac \pi 2 n}}_{n \mathop \in \N }$? --Julius (talk) 17:40, 8 May 2020 (EDT)
Heh! That's an interestingly fun little result to post up sometime: $\dfrac {\d^n} {\d x^n} \sin x = \map {\sin} {x + \dfrac {n \pi} 2}$ --prime mover (talk) 18:08, 8 May 2020 (EDT)

Details of consistency and presentation

Please note we were given a hard time and got some bad press once because one of the big-name mathematics bigshots on one of the big time mathematics websites noticed that we were not entirely consistent in the way we presented the title of the "Also see" sections. We have standardised on "Also see", as you may have noticed. However, at one point we had the occasional page here and there where it was presented as "Also See". This was all the excuse needed by that bigshot to give us a deservedly negative write-up. Hence I would urge you to make sure that if you need to add such a section, to title it "Also see" rather than "Also See". Also, while you are about it, for further consistent look and feel, please note to leave an extra space between sections. I understand how tedious it is to press the enter key an extra time, but it saves a moderator having to go in and fix it. --prime mover (talk) 02:35, 27 May 2020 (EDT)

Will do. Thanks for the feedback. --Robkahn131 (talk) 10:40, 27 May 2020 (EDT)

Proof 1 of Sum of Bernoulli Numbers by Binomial Coefficients Vanishes‎

Presumably you've got a Proof 2 coming?

And I know I keep going on about it, can you learn how the Sources section works? It's because of contributors making a mess of the source citations that we prefer people do not do major refactoring like this until we are certain they know what they're doing.

--prime mover (talk) 16:34, 28 May 2020 (EDT)

I didn't touch or do anything with the Sources. I am not clear on my misstep here. --Robkahn131 (talk) 16:38, 28 May 2020 (EDT)
You copied the Sources section from Sum of Bernoulli Numbers by Binomial Coefficients Vanishes‎ to Sum of Bernoulli Numbers by Binomial Coefficients Vanishes/‎Proof 1, which means there are now 2 pages which link to the same prev and the same next page. It is intended that the flow is a strictly linear total order of the entries in each source work. By copying a source you split the flow.
Obviously when a refactoring job like this is done (as in here, to separate out the proof into a separate page), it is necessary to have access to the actual source work(s) in the Sources section to actually make the flow good. So it is up to someone who actually has these works to fix this (as in: either the proof is included in the source work, in which case the flow will go onto the proof page, or it isn't in which case it's not).
In general we do not split the proof off from the parent page into a "Proof 1" page unless we have a "Proof 2" to add to that page. It's a pain in the arse, there's lots of ancillary work that needs to be done, and it's always Muggins who has to tidy up all that shit, because Muggins seems to be the only one who can understand how this all works (and/or has the attention to detail to make it consistent and correct).
Which is, again, why I ask: you do have a Proof 2 coming, don't you? --prime mover (talk) 16:51, 28 May 2020 (EDT)
I'm afraid I don't. I was actually attempting to be helpful - I see many other pages formatted this way. I sincerely apologize. I really like this site. Shall I put the proof back on the main page and have you delete the proof 1 page or would you prefer I leave well enough alone? Once again - sorry! --Robkahn131 (talk) 17:01, 28 May 2020 (EDT)
In general, there should in fact be very few pages which have a "Proof 1" but no "Proof 2". Which have you identified?
Don't worry, I'll put it all back the way it was.
If a result page and a proof page are separated off into parent-and-transclusion when there is only one proof, that page would be called "Proof" not "Proof 1". If there are exceptions, that usually means someone got so far with putting another proof up but never finished it, or have juggled things around through well-meaning though misguided attempts at being helpful.
One reason to deliberately separate out the proof from the result is if there is a source work which provides a result in one place in the book, then goes off to talk about something else, and then comes back to the result to prove it. To accurately model the source flow it becomes prudent to separate them out. But in that case you would just call it "Proof".
If a need arises to split up the pages like this, they will in general be identified by someone experienced who has a good reason for doing so, and (if they don't change it then and there) will apply the {{Refactor}} template to the page, or whatever other maintenance template may apply.
There are wide gaps in $\mathsf{Pr} \infty \mathsf{fWiki}$'s coverage, and a lot of scope for adding illustrative examples -- most of which that currently exist have been obtained from published works. There should be enough opportunity to considerably expand the content which should not require this radical refactoring of moving big stuff from one page to another. --prime mover (talk) 17:13, 28 May 2020 (EDT)