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.
 * 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.

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.