User talk:RandomUndergrad

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Cheers! prime mover (talk) 10:30, 6 April 2020 (EDT)

Another welcome

Many thanks for your recent work, which plugs some holes. Please keep up the good work.

Please note that I have tinkered with your contributions: mainly for structuring and house style (in particular I feel it is important to put spaces between entities in a $\LaTeX$ construct, as it makes it easier to read and to follow -- the compiler does not care, but neat code is easily maintainable code). Also, I have added a few more explanatory steps on your Equivalence of Definitions of T3 Space so as to make it crystal clear as to what follows from what and why. (I'm getting old and dim.)

Incidentally, I was going to write a program to solve the $1009$, $1129$, $1201$ problem, but you beat me to it. Good job. --prime mover (talk) 04:50, 8 April 2020 (EDT)

Thanks for sifting through those pile of codes! I know there is merit in keeping codes organised, but I think I have a weird mentality where I appreciate seeing structure in others' works, but adopt a minimalistic approach to my own work. (I have been asked numerous times to make my written answers bigger and clearer)

Though I wish to know, how does one find the names (and pages) for the steps in proofs (Empty Intersection iff Subset of Complement, etc.)?

The short answer: knowing they are there, because I put them there.

The long answer: browse the "proofs" category in the subcategory, starting at "Proofs by Topic" where you would expect to find stuff (e.g. "Set Theory" and then within that "Set Complements"), or do a "what links here" for one of the key components in the proof. Yes, it is quite hard work to find stuff till you get a feel for the naming convention. Browse, browse, browse.

It is not intuitive how to get to the bulk of the proofs on $\mathsf{Pr} \infty \mathsf{fWiki}$ by going top-down because we had a clown come on here a few years back who restructured everything according to his own ideas of how he thought the site ought to be structured, and I haven't got round to moving everything back into a new structure where everything's easy to find. --prime mover (talk) 16:25, 8 April 2020 (EDT)

For example, I do not know if ($x^n-y^n$ divides $x^m-y^m$ iff $n$ divides $m$) is an established result. RandomUndergrad (talk) 07:29, 8 April 2020 (EDT)

I don't think that one is. Browse Category:Algebra for results in that area. --prime mover (talk) 16:25, 8 April 2020 (EDT)

Proof Numbering

I did it once (as I recall) in Sum of Sequence of Binomial Coefficients by Powers of 2/Proof 1.

I did it only because this proof is short enough such that everyone can still see the second proof while viewing the first proof (and the statement of the theorem), without having to scroll, so they will know the existence of both proofs. Else it will sit at the bottom and be ignored by the uninterested reader.

If a new proof will not add new insights, I will not add them.

If I add them I will not replace the position of "first proof", unless it is sufficiently short (< 5 lines).

I do not know it is standard practise, if I did it elsewhere please tell me so and I'll reverse the damage. RandomUndergrad (talk) 06:53, 8 May 2020 (EDT)

I put what I said about this on your page by mistake, and you will notice that I immediately removed it when I realised it. --prime mover (talk) 07:50, 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". Many thanks. --prime mover (talk) 02:35, 27 May 2020 (EDT)

changing dfrac to frac

Please don't worry about changing dfrac to frac when you find it in a displaystyle expression or the eqn template. Yes I know it is not needed -- but it if it is dfrac, then it is easier to just copy and paste such an expression into an inline $\LaTeX$ expression without worrying about the displaystyle and without having to amend it.

Yes I know it's inconsistent, but it's not something I am concerned about myself. I don't think anyone else is either. Unless you too are a neatness fanatic :-) in which case feel free to change them as you see them, if you want. --prime mover (talk) 16:08, 21 July 2020 (UTC)

Primitive of Hyperbolic Cosecant Function

Apologies for the mess around Primitive of Hyperbolic Cosecant Function/Inverse Hyperbolic Cotangent of Hyperbolic Cosine Form. Your new proof is at Primitive of Hyperbolic Cosecant Function/Inverse Hyperbolic Cotangent of Hyperbolic Cosine Form/Proof 2.

Usually a good idea to leave a new page for a while before adding a missing proof -- it may be the case that it is being worked on. --prime mover (talk) 08:04, 2 September 2020 (UTC)

Oops. Now the proofs are identical. Although I prefer $u$ and $x$ not appearing in the same integral, please feel free to delete mine. --RandomUndergrad (talk) 08:15, 2 September 2020 (UTC)

Actually that was mine which mixed $u$ and $x$ in the same integral, I did it deliberately so as not to rely on "intuition" to move the proof forward. Making the substitution, then manipulating what results in order to get it all in terms of $u$, rather than manipulating the formula first in anticipation of what the form is expected to be, is not so clear to a newcomer exactly what is being done. It's a matter of taste. While the proofs are very similar, they're not identical, and there's no harm in keeping them both. --prime mover (talk) 08:25, 2 September 2020 (UTC)

mistake in Dudeney

The typo in Henry Ernest Dudeney/Puzzles and Curious Problems/14 - Horses and Bullocks was mine, it was $\pounds 13, 5 \shillings$ not $\pounds 14, 5 \shillings$. I will go through and fix it.

Thanks for your involvement. Cheers --prime mover (talk) 14:41, 20 January 2022 (UTC)

Skeleton puzzles

As you see I have completed my first ever skeleton puzzle, which I found quite hard work. It took me all day.

I would welcome your eyes on this. There may be a far quicker way to solve this than gradually shaving the upper and lower bounds closer, and then explicitly performing tedious calculations to eliminate candidates.

It is moderately interesting that Dudeney missed solution 2. I was only made aware of its existence by the pencilled in notes from someone who had access to my copy of this work before me. --prime mover (talk) 21:52, 27 February 2022 (UTC)

I have finished this puzzle a few days ago, and I did it by bounding $D$ with the help of a spreadsheet. I struggled to find a way to represent the elimination process (or rather, too lazy to type out a table)

So we have done essentially the same thing, and it seems that manually eliminating each possible divisor is inevitable. --RandomUndergrad (talk) 07:59, 28 February 2022 (UTC)

On second reading I found this mistake:

\(\ds \min \set {q_3, q_5, q_6, q_7, q_8}\)

\(\le\)

\(\ds 5\)

\(\ds \leadsto \ \ \)

\(\ds \min \set {q_3, q_5, q_6, q_7, q_8} \times D\)

\(=\)

\(\ds \min \set {p_3, p_5, p_6, p_7, p_8}\)

\(\ds \)

\(\ge\)

\(\ds 1234\)

\(\ds \leadsto \ \ \)

\(\ds D\)

\(\ge\)

\(\ds \dfrac {1234} 5\)

\(\text {(3)}: \quad\)

\(\ds \leadsto \ \ \)

\(\ds D\)

\(\ge\)

\(\ds 247\)

but the minimum is actually $1023$, so $D \ge 205$, and this seems to affect the later steps a little.

Argh! That blows my proof out of the water, as I can't use that to eliminate $Q$ starting with $4$.

For reference I used $1000 > p_1 \ge 900$ to conclude $249 \ge D \ge 225$, so I needed to eliminate those as well. --RandomUndergrad (talk) 08:07, 28 February 2022 (UTC)

Okay, I'll give that some more thought. Trouble is I'm working full time in an office again, and when I get home my eyes are tired and I can't concentrate as well as I might. Getting old sucks. So I may not get to this immediately. If you want to fix it up, please feel free. --prime mover (talk) 19:56, 28 February 2022 (UTC)