User:Jshflynn

About
In time I'll learn to enjoy posting proofs.

For now I find it most relaxing adding sources and references :)

Onwards ProofWiki!

Quicker Typing Help
If you find yourself typing "Definition:" or some other key sequence repeatedly I have found the program AutoHotKeys to be very good:


 * AutoHotKeys website


 * There is also the link in "ProofWiki Specific" right below your edit pane. Saves learning random nonsense. --prime mover (talk) 07:15, 14 December 2012 (UTC)


 * The act of moving one's hand to the mouse, then the pointer to the link below, then click, then move hand back to keyboard is generally more expensive than simply typing the string yourself. Moreover, it presupposes that one does not use an external editor for PW (which I have started to do just a few days ago, the highlighting and improved search/replace functionality make it worthwhile). Thank you Jshflynn, I'll consider it later, when I get home. --Lord_Farin (talk) 12:04, 14 December 2012 (UTC)


 * Each to his/her own - but I have less patience with learning new stuff nowadays. Keeping up with tech is becoming a headache and more than. The links below the edit pane are just what I need. --prime mover (talk) 20:13, 14 December 2012 (UTC)

Thought
In graph theory I think that connectedness of vertices is an equivalence relation and the elements of the quotient set are the components of the graph. If that's true I don't know if it's worth proving. --Jshflynn (talk) 21:04, 21 December 2012 (UTC)


 * It seems to be correct (assuming that connectedness means "exists path" and the graph is undirected). Worth adding, I think. --Lord_Farin (talk) 21:58, 21 December 2012 (UTC)


 * Only in an undirected graph. Funny but I thought I'd already proved this. If not, then go for it because (though trivial) it's important. --prime mover (talk) 22:15, 21 December 2012 (UTC)


 * Aha - seems I have done. Graph Connectedness is Equivalence Relation. --prime mover (talk) 22:17, 21 December 2012 (UTC)


 * Excellent. Had I simply Ctrl F'd 'Equivalence' on the proof index page I would have found it and the corollary that alphabetically precedes it. If you would like a break from the topology section (which is coming along fantastically btw) here's another easy one: "The deletion of a cyclic edge in a complete graph is a complete graph" (the book I am reading at the moment though calls cycle's circuits and what you might think would be called a 'circuitous edge' is just a 'circuit edge', it is from 1981 however so there could have been a terminological shift since then). --Jshflynn (talk) 23:23, 21 December 2012 (UTC)

Deposit
I will have to deposit this here for the future:


 * $\displaystyle\left\vert{ \prod_{j \in J} \left\vert{ \prod_{i \in J} \left\vert{ \left({\mathcal{P}\left({S / \mathcal{R}_f}\right)_j}\right)_i }\right\vert }\right\vert}\right\vert$

Emerging Trends
I am keeping a note here of emerging phenomena on ProofWiki for me to think about. I am aware it is not organised.


 * Theorems that are special cases of other theorems.
 * Definitions that are special cases of other definitions.
 * Processes to generate new theorems (duality principles, the machinery of category theory (corollary spaces?)).

Other undeveloped thoughts:


 * Some theorems are not used in the proof of anything else. Perhaps have community consequence challenges? The players have to prove something else using the theorem at least once.


 * Just noticed this. I don't see this as being a problem. Certain theorems are "end points" in that they exist as an end in themselves. FLT is an example I can think of (although you'll tell me it has a use now).


 * Lemma (or Exercise) namespace? The idea being that people store answers to questions in books so that more people can have a go of using LaTeX and wikis (the book in question of course not having the answers). Reward users by saying that their work has been "promoted" to the theorem namespace and let them know that they too can do mathematics. This way the theorem namespace isn't cluttered and it's getting others involved.


 * Lemmas should carry on existing in the Theorems namespace, because it's not a hard-and-fast rule as to what is a lemma and what is a theorem. Lemmas are identified (usually) by having "Lemma" at the top instead of "Theorem".


 * Examples I'm less sure about. What I am sure of is that I would rather they did not clutter up a definition page (or proof page, come to that) but should have standalone pages. What we could do is have example categories as subcategories of either theorem or definition categories (but I understand that the namespace paraduigm may be compromised by the latter - does that matter?) There could be a specific template that would go into an "example" category like we have in the existing categories and subcategories. But I haven't gone down that route because the concept of examples in general (except for the instances of topologies and groups etc.) does not interest me much. --prime mover (talk) 19:46, 18 January 2013 (UTC)

Antitransitive Implies Antireflexive
Let:


 * $xy,yz \vert \overline{xz}$

Suppose:


 * $aa$

Then:


 * $aa,aa \vert \overline{aa}$

A contradiction.

Hence:


 * $(xy,yz \vert \overline{xz}) \vert (\vert \overline{xx})$

$\blacksquare$

Deposit 2

 * $\begin{xy}

<0em,0em>*+{M_n(\mathbb{R})} = "S1", <5em,0em>*+{M_n(\mathbb{R})} = "S2", <5em,-5em>*+{\mathbb{R}} = "S3",

"S1";"S2" **@{-} ?>*@{>} ?*!/_1em/{t}, "S2";"S3" **@{-} ?>*@{>} ?*!/_1em/{\operatorname{det}}, "S1";"S3" **@{-} ?>*@{>} ?<>(.4)*!/^1em/{\operatorname{det}}, \end{xy}$


 * I would advise you to use xymatrix instead. It allows to focus more on semantics rather than syntax. --Lord_Farin (talk) 08:15, 16 January 2013 (UTC)


 * Good advice. You may want to change the Definition:Commutative Diagram page if this is the case as this is where I got it from. :) --Jshflynn (talk) 09:46, 16 January 2013 (UTC)


 * Thanks for the pointer. Done. --Lord_Farin (talk) 19:03, 16 January 2013 (UTC)

Deposit 3
Captain's log: I have managed to open the database. There is a lot of excess data in there.


 * Managed to create a program which can output:


 * Set: Object, Element, Comprehension Principle, ...


 * I am leaving it to run in the background. It will take about 6 hours.


 * Ugh. Came back to PC and there was an error with the 2000th file. Getting there though...

From there I will see if I can make the GML script.

Deposit 4
Definition:Lambda Term

Progress
So I have the necessary data to make the graph.

For phase 1 I will just be making a simple graph that shows the connections between the definitions.

For phase 2 I'm going to colour the nodes according to their category. There are two problems though:


 * 1. Deciding on the colouring scheme.


 * 2. One very notable contributor on here is colour blind so I will have to find some way around that.

Stay tuned.

Progress 2
So here is what I'm working with:

Proofwikiwords

It is incomplete because proofwiki is not yet perfectly monolithic (in the words of PM) and I want to get the project moving. I believe it is sufficient to give a simple overview :)


 * First impression: very smart.


 * Can you find places in it where it is inaccurate / incomplete because of ProofWiki's lack of being completely monolithic? That is, can it be used to provide direct feedback on PW's tightness and internal cohesiveness? --prime mover (talk) 19:38, 18 January 2013 (UTC)


 * Very cute, indeed.
 * One apparent problem: the dictionary doesn't look at subpages. For instance, the entry for the word coprime is empty. This is because the page Definition:Coprime has been refactored to a degree that it doesn't link to anything but subpages, which isn't registered in the dictionary.--Anghel (talk) 19:47, 18 January 2013 (UTC)


 * Essentially my Macro is hunting for sections on definition pages that are headed by either "== Definition ==" or "== Formal Definition ==". It then pulls out what it sees as valid links from inside those sections.


 * There are some sections that are headed by "== General Definition ==" instead which is perfectly valid, I just had never seen them before.


 * I think I should take back what I said as looking further into it the whole problem seems to be with my program handling redirects and subpages. I think I will leave this for phase 2 though as I'm rather impatient to see if the "convert list to graph" stage of the project is actually doable. --Jshflynn (talk) 19:54, 18 January 2013 (UTC)


 * Neat stuff. Might be good to look into the fact that some listings end with a comma while others don't. --Lord_Farin (talk) 22:08, 18 January 2013 (UTC)
 * Another one: rendering of non-UTF8 chars like letters with accent and Scandinavian, Polish letters. --Lord_Farin (talk) 22:10, 18 January 2013 (UTC)


 * How coincidental that I was attending to the comma issue just now before I read this. You have the instincts of a programmer it seems. Thanks for the heads up on those accents, I don't think anybody would be to pleased seeing "G?nter" or something of that sort where their name should be :) --Jshflynn (talk) 22:17, 18 January 2013 (UTC)