# User talk:Jshflynn

## Contents

- 1 Welcome
- 2 Title style
- 3 Editing section-wise
- 4 Nudge
- 5 Motivation?
- 6 Rework?
- 7 Broken link
- 8 Other Languages
- 9 Appointment
- 10 Dictionary of Mathematics
- 11 book links
- 12 Coretraction
- 13 Spot the flaw or salvage the group
- 14 Jordan Curve Theorem
- 15 Metamath
- 16 \restriction
- 17 *ping* Subband of Induced Operation is Set of Subbands
- 18 Equation template and all that
- 19 Schröder Rule
- 20 What is the point?
- 21 Colon
- 22 Prev next work
- 23 Extra blank line
- 24 Hungerford book

## Welcome

Welcome to ProofWiki! Since you're new, you may want to check out the general help page. It's the best first stop to see how things are done (next to reading proofs, of course!). Please feel free to contribute to whichever area of mathematics interests you, either by adding new proofs, or fixing up existing ones. If you have any questions please feel free to contact one of the administrators, or post your question on the questions page.

Here are some useful pages to help get you started:

- Community Portal - To see what needs to be done, and keep up to date with the community.
- Recent Changes - To keep up with what's new, and what's being added.
- Check out our house style if you are keen on contributing.
- Main Page talk - This is where most of the main discussions regarding the direction of the site take place. If you have any ideas, please share them!

Cheers!

- --Your friendly ProofWiki WelcomeBot 10:10, 2 May 2012 (EDT)

## Title style

Note the house style when it comes to titles: important words are capitalised. What will happen is that someone will go through and change the titles of some of your recent pages as appropriate. Getting a good title for a page is an art so you may find the pages you've written may get namechanged.

Please keep up the good work - you are filling gaps we did not know we had. --prime mover 23:57, 19 July 2012 (UTC)

Thanks prime.mover. It is indeed difficult especially for something as unnameable as a B-Algebra identity. The true credit goes to others though. Someday I hope to publish my own paper so that I can see my own ideas on relation theory on this wiki. For now though I will continue research as too often I have found that any original idea of mine has been analysed to death in an obscure research paper. --Jshflynn 00:23, 20 July 2012 (UTC)

## Editing section-wise

Although convenient, the section-wise editing feature destroys the carefully set up large whitespace separating sections. This then requires a subsequent edit to recover the desired amount of white. It is therefore generally preferable (except on talk/user pages, where house style is not enforced) to edit the page as a whole using the link at the top. --Lord_Farin 21:48, 21 July 2012 (UTC)

I see. Will do so for my next edit. --Jshflynn 21:53, 21 July 2012 (UTC)

## Nudge

To avoid reinventing the wheel, consider Category:Definitions/Formal Systems. --Lord_Farin 23:48, 9 August 2012 (UTC)

That's alright. If I make something worthwhile then I will. --Jshflynn 23:49, 9 August 2012 (UTC)

## Motivation?

"I honestly wish I had never discovered mathematics."

I'm glad I did, because I'm even more incompetent at everything else. --prime mover 06:40, 10 August 2012 (UTC)

## Rework?

Not meaning to pour cold wet water-based liquid on your flames, but a lot of the stuff you're adding to your "Definitions" section has already been documented in the Category:Definitions/Formal Systems category (admittedly not that well structured at the moment). I'm not sure whether you're trying deliberately to reinvent this area of mathematics from a different viewpoint (full respect due) or whether you're not familiar with this area yet. Just sayin' ... --prime mover 11:53, 10 August 2012 (UTC)

- Sorry - I see L_F has already been here. No worries. --prime mover 11:54, 10 August 2012 (UTC)

- I am reading a book on Formal languages and computation at the moment. It says that a lot of concepts are clear/obvious. I also noticed you, L_F and a few others seem to process your books by putting them on a completely rigorous basis on this site. As you are so successful at doing so and I am so unsuccessful at finishing books I decided to adopt the same approach.

- The definitions on the section of this site clashed with a lot of the things I was reading (most likely because the field in question isn't that standardised). So, I decided to create my own user-based section in order to not mess up the work someone else did. Right now, it's really just the theory of finite sequences. But in due time it might look better. --Jshflynn 12:24, 10 August 2012 (UTC)

- It is often the case that different books do things in different ways, partirulcarly in evolving fields like mathematical logic and formal systems. What the approach is that we want on this site is to gather the various different approaches into one by using the "also known as" and "also defined as" technique: the first if the same concept is called by something different, and the second if either (a) the same name is used for two different things, and (b) (more tricky to do rigorously) if it's the same concept but defined with a subtle difference in the conditions (something in topology comes to mind where certain objects are defined on "open sets" by one source and "not necessarily open sets" in another).

- The problem of course lies in the fact that proofs based on the definition in format A may well not work using the definition in the format B. Then we get angry emails from people who assume (without checking) that the proof assumes format B. The only way round this is to ensure rigorous proofwriting so that when an ambiguous property of an object is used, it is stated as well as being linked to. --prime mover 07:38, 16 August 2012 (UTC)

- Oh yes, and it's also got to be pointed out that some books are not very good (in terms of rigor), if they are designed as a basic introduction for popular consumption. IMO this over-simplification approach might not be appropriate for ProofWiki. But as the book you are quoting from hasn't been specified, it is not possible to say whether this applies in this particular circumstance. --prime mover 07:42, 16 August 2012 (UTC)

## Broken link

The link you put on the community portal does not work. --Lord_Farin 06:33, 16 August 2012 (UTC)

- Fixed it, moved it into the appropriate place. --prime mover 07:38, 16 August 2012 (UTC)

## Other Languages

I'm so happy you took the initiative with German here on ProofWiki. I know I'd love to do something with the Hindi or Spanish portions, but I am currently tied up at work. My whole goal was to diversify ProofWiki and you've helped it get started. Maybe after things settle I could ask ask you again. I thank you once again. --Smettems (talk) 01:09, 8 October 2012 (UTC)

## Appointment

You seem to have missed our virtual appointment; it happens. It's just that I had been looking forward to it. --Lord_Farin (talk) 22:23, 27 October 2012 (UTC)

## Dictionary of Mathematics

You are (to considerable benefit) adding references to the "Dictionary of Mathematics". As you may or may not have noticed, it is standard that some indication is provided as to where in a source the concept under consideration is (first) encountered. IMO, it would benefit the significance of your exercise if you included this. --Lord_Farin (talk) 09:27, 6 December 2012 (UTC)

- No problem. In the dictionary I found "exterior multiplication" in the entry "module". So would:

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*: ref. pending

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:

- Become:

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*: Entry: Module

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:

- That seems like an adequate solution. --Lord_Farin (talk) 10:21, 6 December 2012 (UTC)

- Why "Entry"? How about just:

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*: Module

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:

- with perhaps highlighting of the entry itself by making it italic (? maybe). Also note that in the case (like this) where the reference is to a concept held on ProofWiki on a different page, make it a link:

- Suggestions only. --prime mover (talk) 11:37, 6 December 2012 (UTC)

- The "Entry:" addition is clarifying IMO. The amalgamation:

- : Entry:
*Module*

- has my vote (possibly without italics). --Lord_Farin (talk) 12:25, 6 December 2012 (UTC)

- Might be worth adding an option to the BookReference template, e.g. "entry=..." which, if present as e.g. "entry=Module", will automatically add ": Entry:
*Module*". Mind, last time I tried editing this template it started adding spurious linefeeds in the rendition, which I couldn't work out how to eliminate, so that may not be immediate. Then, if we decide on a different format, we need to change it in one place only. --prime mover (talk) 12:54, 6 December 2012 (UTC)

- Might be worth adding an option to the BookReference template, e.g. "entry=..." which, if present as e.g. "entry=Module", will automatically add ": Entry:

Due to some spare time being consumed atm anyway, I have implemented the suggested feature:

`* {{BookReference|Dictionary of Mathematics|1989|Ephraim J. Borowski|author2=Jonathan M. Borwein|entry=Module|entryref=Definition:Module}}`

ought to produce:

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*: Entry:**Module**

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:

...and after a subsequent edit, it does. --Lord_Farin (talk) 13:12, 6 December 2012 (UTC)

It appears the spurious line breaks are due to MediaWiki interpreting a colon at the start of some piece of text (e.g. in an if clause) as were it positioned at the start of a line, causing a newline and indentation. Nowiki tags resolve the issue. --Lord_Farin (talk) 13:14, 6 December 2012 (UTC)

- Excellent. --prime mover (talk) 14:23, 6 December 2012 (UTC)

## book links

10/10 for enthusiasm, but preferable to post up the details of the book (and its authors)you are adding citations for before you add the citations - otherwise it's a great big pile of redlinks. I know, it can be a tedious task (specially if you don't have an ocr) to fill in the contents list, but you'll probably find that you may be the only active ProofWiki worker who has the book in question. --prime mover (talk) 06:12, 10 December 2012 (UTC)

- In addition to that, please note that the sources are ought to be in chronological order. --Lord_Farin (talk) 09:04, 10 December 2012 (UTC)
- I found the time to correct the order on all pages you have added the source for now. --Lord_Farin (talk) 09:11, 10 December 2012 (UTC)

- Why is it inconvenient? You enter the definition, you enter the theorem, and you thread the links in the opposite order. Where's the problem? --prime mover (talk) 21:22, 10 December 2012 (UTC)

- My mistake. I was under the impression that the (Previous)...(Next) feature had to respect the presentation of the book exactly. Perhaps it strays from the aims of ProofWiki but is there someway to see a list of all definition pages with no sources subsection? --Jshflynn (talk) 22:26, 10 December 2012 (UTC)

- The way I implement it, the (Previous)...(Next) feature does respect the presentation of the book exactly. So the (previous) link of (definition of concept A) is (theorem proving existence of concept A) and the (next) link of (theorem proving existence of concept A) is (definition of concept A). As I say, where's the problem? --prime mover (talk) 22:32, 10 December 2012 (UTC)

- Why do you need a list of all the definition pages with no sources subsection? --prime mover (talk) 22:33, 10 December 2012 (UTC)

- Would you rather learn theorems pertaining to A or the definition of A first? If it is immaterial to you then there is no problem and I see now it's just personal preference that I would rather learn a definition first.

- Perfectly rational to prove the existence of an object, then after you've done that, give it a name. That's how the mathematician who discovered such an object probably worked it. Oh look, if you perform that operation to this object you get such-and-such an object. I'll define it thus-and-so. --prime mover (talk) 23:22, 10 December 2012 (UTC)

- It would be interesting to see which concepts are local to ProofWiki, which are too old to admit a citation, which are too general etc. ProofWiki is both a large and structurally regular body of information. It is only natural that I want to see patterns and statistics behind it. --Jshflynn (talk) 22:51, 10 December 2012 (UTC)

- Most interesting. I didn't know you could do that with a rectangle. DHEI is half the area of ABCD. I wonder what would happen if you plotted all the "potential" E points such that that relationship holds. Is E somewhere special on the curve you obtain? --Jshflynn (talk) 23:53, 10 December 2012 (UTC)

- Yes it is. That's the whole point. It's the incentre of that triangle. Unique for a given rectangle. --prime mover (talk) 06:11, 11 December 2012 (UTC)

- Beg pardon, see what you mean. The locus of all the points $E$ such that $\Box DHEI = \Box ABCD / 2$. Should be straightforward to work out algebraically. My guess is that it's a quarter of an ellipse. --prime mover (talk) 23:07, 11 December 2012 (UTC)

D'oh! It is of course a hyperbola. Letting $(x, y)$ be the corner of the rect in question and letting the total area of rect be $ab$ the locus is of course described as $xy = ab/2$ which is a trivially simple example of $xy = c$. --prime mover (talk) 20:23, 28 December 2012 (UTC)

## Coretraction

Really? Definition:Section (Category Theory) referred to as **coretraction**? What source? (The use of "section" and "retraction" easily predates the entirety of CT.) --Lord_Farin (talk) 08:35, 18 January 2013 (UTC)

- Cf. Barry Mitchell: Theory of Categories. Sorry L_F its such a pain setting up a source work I just assumed it was used throughout CT. You may remove at will. --Jshflynn (talk) 09:28, 18 January 2013 (UTC)

- Well, as long as there exists a source, I won't remove it. I understand you're not going to bother writing up the whole source at this point; we all do what we do best. --Lord_Farin (talk) 09:35, 18 January 2013 (UTC)

- I have taken the liberty of adding the source work, as well as the mathematician. Note that I can't find out when or where Barry Mitchell was born, so I'm guessing America 1930. He needs more of a page than an "Author" as there's at least one theorem named after him. --prime mover (talk) 17:01, 8 March 2013 (UTC)

- ... this wrk has now been invoked on the page in question.

## Spot the flaw or salvage the group

So the other day I thought I had found something isomorphic to the Klein 4 group.

My idea was to take all the statements generated by the grammar of propositional calculus and partition them into equivalence classes using the relation of logical equivalence.

Then, because every statement can be written in disjunctive normal form it can also be written with implication as its main connective (by the equivalent definition of disjunction).

So perhaps I could have functions on these equivalence classes that are based on the notions of converse, inverse and contrapositive.

It came from seeing the statement 'the inverse of the converse of a statement is its contrapositive'.

Naturally, we get the table below:

- $\begin{array}{|c||c||c||c||c|} \hline \text{Composition} & \text{Inaction} & \text{Conversion} & \text{Inversion} & \text{Contraposition} \\ \hline \text{Inaction} & \text{Inaction} & \text{Conversion} & \text{Inversion} & \text{Contraposition} \\ \hline \text{Converse} & \text{Conversion} & \text{Inaction} & \text{Contraposition} & \text{Inversion} \\ \hline \text{Inversion} & \text{Inversion} & \text{Contraposition} & \text{Inaction} & \text{Conversion} \\ \hline \text{Contraposition} & \text{Contraposition} & \text{Inversion} & \text{Conversion} & \text{Inaction} \\ \hline \end{array}$

As much as one would like the table to be true and for this to be a rather quirky result to add to the database there is one massive and obvious flaw to it.

See if you can spot it or better yet salvage the group. --Jshflynn (talk) 22:17, 25 January 2013 (UTC)

- Nope, can't spot the flaw. Looks like a Klein 4 group to me. --prime mover (talk) 22:40, 25 January 2013 (UTC)

- That's what I thought, but the functions aren't well defined. For example, for inaction composed with inaction I could put inaction
**or**contraposition. It's to do with how I've defined the underlying set.

- That's what I thought, but the functions aren't well defined. For example, for inaction composed with inaction I could put inaction

- There are no flaws. You just need to define the entities appropriately. It's just an instance of composition of mappings. --prime mover (talk) 23:03, 25 January 2013 (UTC)

- Please explain:

- Contraposition $\circ$ Contraposition = Contraposition

- Contraposition $\circ$ Contraposition = Inaction

- Sorry, just noticed this is unresolved: how is Contraposition $\circ$ Contraposition = Contraposition? No comprendo. --prime mover (talk) 12:31, 2 February 2013 (UTC)

## Jordan Curve Theorem

I've seen that you've put up definitions of the Jordan Arc and Curve. Do you intend to upload the Jordan Curve Theorem as well? I'm going to need that in the Complex Analysis section. It would be nice if we could work together on a formulation of this theorem. --Anghel (talk) 11:59, 2 February 2013 (UTC)

## Metamath

As I'm a big fan of people learning much better when given the opportunity to find out for themselves, I will do no more here than make the observation that there has been a metamath citation template in existence for some time. You are encouraged to hunt down the appropriate page in the Help suite, in particularly that pertaining to House Style. --prime mover (talk) 07:37, 8 February 2013 (UTC)

## \restriction

The intended use of $\restriction$ is as on Definition:Restriction/Operation. Unfortunately, Definition:Subsemigroup wasn't a good source to copy-paste from. — Lord_Farin (talk) 22:00, 6 March 2013 (UTC)

## *ping* Subband of Induced Operation is Set of Subbands

Please complete said page. — Lord_Farin (talk) 13:31, 7 March 2013 (UTC)

## Equation template and all that

When putting an equation up in the equation template, you need to be careful to avoid including `{{`

, `}}`

and `|`

symbols. The reason is apparent if you think about it.

In such cases, you put a space between the braces, and instead of `|`

you use `\vert`

.

This is documented in the Template:Eqn page but I think I need to put it in the FAQs too, because this keeps coming up. --prime mover (talk) 08:38, 8 March 2013 (UTC)

- In the unlikely case a pipe (|) is needed outside math environment, use Template:!, i.e.
`{{!}}`

. — Lord_Farin (talk) 09:42, 8 March 2013 (UTC)

## Schröder Rule

I cleaned up what I believe were mistakes in the partial proof. We still need to finish it. Also, there's a claim right at the beginning that $A \circ B \subseteq C$ means, by the definitions of composition of relations and subset, that:

- $\forall x, y, z \in S: \left({ (y, z) \in A \land (x, y) \in B \implies (x, z) \in C }\right)$

However, the definitions only get us to

- $\forall x, z \in S: ((\exists y: (y, z) \in A \land (x, y) \in B) \implies (x,z) \in C)$

So we need some sort of theorem of predicate logic to bridge that gap. Want to give it a go?

Finally, I personally don't much care for truth table proofs escaping from the propositional logic category. Could that part be factored out as a proplog lemma? --Dfeuer (talk) 21:37, 28 May 2013 (UTC)

## What is the point?

What is the point in adding a same proof in 1+1 = 2/Proof 2? --Kc kennylau (talk) 07:11, 6 July 2013 (UTC)

## Colon

Don't forget the colons between the Template:BookReference and the relevant section when adding references. I take it that you will get round to creating the book and mathematician page in due time? — Lord_Farin (talk) 17:33, 23 July 2013 (UTC)

- Also, you need to be careful when you link to a page with subpages - you need to go back and add the subpage into the link from the previous page or the thread gets lost.

- Also, that book is styled as by "Thomas W. Hungerford", not "Thomas William Hungerford", so these pages will need to be revisited on that account as well. --prime mover (talk) 19:14, 23 July 2013 (UTC)

## Prev next work

When you come back after breaking off, don't forget to go back and add the "Next" tag to the last page you left with just a "Prev" tag. The best approach is to include the next tag along with the prev tag on the last page of an editing session, rather than put just a "prev" tag up, so you don't forget stuff like this. --prime mover (talk) 20:12, 25 July 2013 (UTC)

- And like I said the other day, don't forget to go back and add the subpage to the "next" link on a page which has subpages, like I just did on the "next" link on Integers Modulo m under Multiplication form Commutative Monoid. I appreciate what you're doing here, but this stuff needs care to be taken.

**Please**take note of this point, I keep finding I have to go back and fill the "next" in for you. I'd rather not have to do that tedious job. --prime mover (talk) 19:14, 27 July 2013 (UTC)

## Extra blank line

Please note this:

I specifically mention it because it appears to be a detail of the house style that has passed you over. Please note that, in order to improve the presentational quality of pages, there is an extra blank line between all sections. --prime mover (talk) 06:10, 30 July 2013 (UTC)

- And while I'm about it, there's no blank line above the $\blacksquare$ at the bottom of the proof. Please put the
`{{qed}}`

tag on the line*immediately*below the end of the proof. Again, it's just house style, it improves the look. --prime mover (talk) 06:18, 30 July 2013 (UTC)

## Hungerford book

Also, the contents of the source work which you are building up as a list in your user space is not in the format in which books are presented in the Books section. I mention this in case you are planning on putting it up in the "Books" section as the forthcoming Book:Thomas W. Hungerford/Algebra page.

This page needs to be structured as the contents list of the book as it is published. Please see examples of this. I appreciate it may look like a lot of work, which is tedious. You're right, it is. Get an OCR and scan the pages in, then all you need to do is tidy them up. --prime mover (talk) 06:24, 30 July 2013 (UTC)

- The page User:Jshflynn/Hungerford Algebra is for myself. I have made the page Book:Thomas W. Hungerford/Algebra with the skeleton of the contents. I will fill the contents out in more than one session. --Jshflynn (talk) 08:31, 30 July 2013 (UTC)

- Good stuff. Note the use of "text" form of section headings: $\text{I}$, $\text{II}$ etc., and also, in books contents we don't use bullets (they look untidy), just indents, which are also easier to manage. --prime mover (talk) 08:58, 30 July 2013 (UTC)