User talk:Joe

This is a test of the user notification system. When someone writes on your user talk page, you get notified. --Miike 18:17, 23 July 2008 (UTC)

Awesome! Check out the Powers of Commutative Elements in Semigroups‎ page, where this technique has just had its baptism! Okay so it's a bit of a weak proof but it shows how neat and compact it is. Be aware that I'm a neatness freak btw, readability of source code is 100% as important as readability of the end product, which explains my fussiness over formatting. --Matt Westwood 19:04, 19 October 2008 (UTC)

Awesome, looks good! --Joe 19:13, 19 October 2008 (UTC)

Yo, did you add Payne's signature manually, or did you log in to his account? --Cynic 17:06, 22 November 2008 (UTC)

manually, just looked at the timestamp from the history log. I can't get access to accounts, passwords are protected with MD5. --Joe 18:05, 22 November 2008 (UTC)

Hey, save it for April Fools Day Proof of the Week :D --Cynic 17:45, 26 November 2008 (UTC)

Very, very subtle. Still trying to put into words exactly what goes wrong and why ... --Matt Westwood 19:30, 26 November 2008 (UTC)

What to do?
For one "Topic" i must write one theorem with the respective proof? or can I write more than a theorem? For example the area of a triangle have alots of formulas then i have write a "topic" with each of the formulas or only in one "topic"

thk gamma

Good question, I guess what I would do would be either:
 * 1) Do a separate page for each one with good descriptive names and put them inside of a new area of triangle category inside euclidean geometry category, or
 * 2) put them all on one single page and use formatting similar to what I've boxed in below.
 * 3) Another thing would be to do the first option, then transclude all those separate proofs onto a single page using  to dump the content from that page. Then use idea 2 to organize them.
 * 4) The last thing I can think of is use an approach similar to Trigonometric Identities.

Theorems
For any triangle ABC with sides a,b, and c, the area of ABC has the following properties:

Area Equal to some formula
Statement

Some other statement wrt area of ABC
Statement ...

Proof that statement 1 is true
proof

Proof statement 2 is true
proof ...

Those are the only things I can think of. With something like that were's there several formula it's pretty well open ended what you want to do with it. If anyone else is reading this and has an opinion or idea please comment. Hope this helps! --Joe 03:27, 30 December 2008 (UTC)

Well, personally I think it makes sense to have separate pages and maybe transclude them. That way we can have a seperate page for Heron's Formula (or Hero's Formula if you prefer), since it at least belongs in Named Theorems.

For the moment, I would just put it up in whatever format seems most comfortable for you, and we can worry about organization later. --Cynic-(talk) 05:10, 30 December 2008 (UTC)

good call. --Joe 15:46, 30 December 2008 (UTC)

Geometry euclidian or analytic ?
well i have a new problem.. what happens if there is a theorem of euclidian geometry but the proof was made with "analytic".(by "anlytic" i understand, for me ,in geometry, is use vectors) --Gamma 22:43, 31 December 2008 (UTC)

The fact of a proof being valid in a flat space (as opposed to elliptic or hyperbolic) means (to me) that it's a Euclidean Geometry theorem. The fact that it's proved by a Cartesian method should not matter. Thoughts? --Matt Westwood 23:03, 31 December 2008 (UTC)

okokoooko i forget that we can put one topic in two difernt categorys =O -- Gamma 23:15, 31 December 2008 (UTC)

NUM pages
I actually think it makes more sense to copy and paste the message. That way people who are relatively new to wikis won't be confused by seeing when they edit their user talk page. That said, if you want to make a template, feel free. --Cynic (talk) 20:26, 10 March 2009 (UTC)

Rename request?
Hi, Joe. I was hoping you could change my username? I want to use my real one, that is, J D Bowen or J_D_Bowen.

Done! --Joe (talk) 23:43, 27 April 2009 (UTC)

Thank you! J D Bowen 19:07, 28 April 2009 (UTC)

New page?
Okay so you've proved $$1<\gcd(x-y,n)<n$$ and $$1<\gcd(x+y,n)<n$$ ...

Because $$\gcd(x-y,n) | n$$ then $$\gcd(x-y,n) \le n$$ anyway because of the nature of Integer Absolute Value Greater than Divisors.

So all this says is that $$x-y \ne n$$ or $$n \mid (x-y)$$, and $$(x-y)$$ is not coprime to $$n$$.

But I'm looking at this and surely $$x^2\equiv y^2\pmod{n} \implies x \equiv \pm{y} \pmod{n}$$?

So I'm not sure if the premise can ever be true in the first place.

I may be completely wrong - can you think of any $$x, y, n$$ such that $$x^2\equiv y^2\pmod{n}$$ and $$x \not \equiv \pm{y} \pmod{n}$$? --Matt Westwood 15:01, 24 May 2009 (UTC)

Goodness so it is. How about something like "Limits of GCD for Sum and Difference Congruent Squares" or something vague like that?

I'm wondering whether you can prove something stronger, but no worries ... --Matt Westwood 15:35, 24 May 2009 (UTC)

been away
In case you wondered where I've been, I had internet connection problems since Monday (stupid ISP). I'm back. --Matt Westwood 21:50, 18 June 2009 (UTC)

I was starting to get worried :p --Joe (talk) 11:40, 19 June 2009 (UTC)

Five Color Theorem
I think I finally got it sorted out fully. Take a look and let me know if it looks right so we can take it off wanted proofs. --Cynic (talk) 04:00, 30 June 2009 (UTC)

Looks good to me --Joe (talk) 01:58, 8 July 2009 (UTC)

I'm slowing down ...
Just in case you're worried I've died or something ...

I've gone about as far as I can go for the moment on the elementary stuff. Notes on the following:
 * I got tied up in knots and bogged down in the predicate logic stuff. I need to go away, do some reading, do some work and formulate the best way to proceed before I can go any further (and probably backtrack big time). Maybe someone else with a better background in formal systems might want to pick up on it. My own knowledge in this area is primitive and self-taught.


 * I have it in mind to do something to flesh out basic Graph Theory, but you already have someone on that particular case.


 * I could also continue with Euclid, but that's also being covered.


 * Then there's statistics and probability, which I don't like (despite the fact of it being merely an extension of boolean algebra -- strangely enough I've never seen that fact stated anywhere).


 * I have it in mind to start with some applied maths (after all, there's no point covering diffeqs without applications), but it's too big a job for me at the moment.

Basically, the current economic and industrial / professional climate being what it is, I'm going to need to work on some projects of my own for a while, as I really need to get some more strings on my bow / keep the bread and butter coming in.

I'll keep dropping in, and putting a theorem / biog / definition up here and there, and keep on with the tidying up, but I'm not going to be anywhere near as busy as I have been in the past year or so.

I've sent the same message to Cynic.

all the best --Matt Westwood 20:28, 26 July 2009 (UTC)

Sounds good, now the rest of us won't look so bad ;) --Joe (talk) 00:09, 27 July 2009 (UTC)

Re : Welcome
Thanks :) I spotted Tychonoff's Theorem on the Most Wanted List and thought I'd give it a go since I recently did an exam on topology. After quite some background stuff (required for the ultrafilter-approach I'm going to use) I'm almost ready to prove the theorem itself. Florian Brucker 14:09, 25 January 2010 (UTC)