User talk:GFauxPas/Archive1

Convergence and other principles of analysis
Currently I am a teaching assistant for an advanced analysis course, so if you have any questions regarding real (multidimensional or not) analysis, feel free to drop a note on my talk page. When you eventually get there, I might be able to help out on Complex Analysis as well. --Lord_Farin 14:27, 23 October 2011 (CDT)

Awesome, thanks a lot --GFauxPas 14:33, 23 October 2011 (CDT)

Notation
I note from your front page you're setting up some copypasta for yourself. Before you go too far down that route, pls note the following:

1. The raw symbols ≡, · and Δ and so on are never used on ProofWiki. The $\LaTeX$ code is always used: $\equiv, \cdot, \Delta$ (or when appropriate $\triangle$ and its variants).

2. For "defined as" we use $:=$ as this is a specific symbol meaning "is defined as". The $\equiv$ symbol has plenty of other meanings and it is best kept for those.

Hope this is OK. --prime mover 16:29, 24 October 2011 (CDT)

A while back I wrote a proof that all integers are even or odd. The reason I wrote it was just to practice mathematical induction. The theorem itself seems rather unimportant, and so I don't see a reason to make a page for it, but at someone's request I can make it. --GFauxPas 15:56, 4 November 2011 (CDT)
 * I have a feeling that one might already be up, but I don't think it was proved by induction. Can't remember and I don't feel like looking at the moment. --prime mover 17:24, 4 November 2011 (CDT)

Seeing as how we're using an uncommon notation for intervals to avoid ambiguity, what's the defining criterion for whether we use an atypical "better" notation or not? For example, the though the standard notation for function inverse is $f^{-1}$, that notation is the same as that of the multiplicative inverse, very different things. There's $f^\gets$ and $\breve f$ which aren't ambiguous, but they're not common. --GFauxPas 16:41, 8 November 2011 (CST)


 * Good question. There are many notations for intervals, and none of them are very good because it's easy to mistake two numbers separated by a comma for all sorts of other usages. $[a..b]$ is not common but it's completely unambiguous and has a precedent in computer languages, so I'm sort of expecting it to catch on. Getting mathematicians to change their notation, though, is not easy.
 * As for the inverse function notation, "generally speaking" you don't mistake $f^{-1}$ for a multiplicative inverse because the contexts are different. The $f^{\gets}$ notation has been noted on the page for inverse mapping so I suppose we could start using it, if you particularly like it. --prime mover 17:05, 8 November 2011 (CST)


 * I think I oppose to that. The notation for the interval isn't really ambiguous, even if you never saw it before, the meaning is clear. With $f^{\gets}$ I am having the hunch that it will create unnecessary fuss. But that's me, and probably an instantiation of the notation change thing... --Lord_Farin 17:09, 8 November 2011 (CST)

Lord_Farin, just wanted to let you know that I figured out your explanation and PW's approach here Talk:Fundamental_Theorem_of_Calculus/Alternative_Second_Part_Proof, thank you! --GFauxPas 22:19, 5 November 2011 (CDT)


 * Glad I put up sensible stuff. HTH --Lord_Farin 09:01, 6 November 2011 (CST)

Talk page etiquette
I hate having to keep calling you out like this, I sort of hope you will pick up the conventions as you see them being used.

However, it's probably worth mentioning the usual protocol in talk pages, when there's a conversation going on.

You may have noticed that when you start a line with a colon it acts like a tabulator, that is, indents the line by a fixed and noticeable amount. Starting with more colons indents the line further.

Anyway, in a talk page the convention is to start each reply with one colon more at the start of the line. In that way it can be easily worked out who said what, and when they said it, and what they are replying to. Only when the indentation becomes too much (usually about 7 or 8 colons in) is the conversation reverted to the far left hand side of the page again. Usually this does not happen on ProofWiki because issues are usually solved within two or three postings. --prime mover 12:34, 11 November 2011 (CST)
 * Noted. Sorry to disappoint. I'll cop out and play the "not sleeping enough" card. --GFauxPas 12:41, 11 November 2011 (CST)

Real Number Line
Good job! A couple of things:

a) Tarski may well have been making unwarranted assumptions when he wrote this proof, and/or mathematics has moved on since his day. However, I believe it's not enough to just state that there exist mappings between the two sets for there to be a bijection between them - we need to show they are injective. After all:
 * $A = \{0, 1\}, B = \{2\}, f: A \to B: f(0) = 2, f(1) = 2, g: B \to A: g(2) = 0$

fits the conditions: $f$ and $g$ are both mappings, but $A$ and $B$ are definitely not equinumerous.

b) From the words put forward by Qedetc in the talk page, it appears that Tarski may have defined some axioms in order for assumptions on this page to be valid. Qedetc was insistent that no such mapping could possibly exist without such, but I was not able to pin him down on exactly what needed to be done. Can you read that book carefully (or do further research) to see whether there's something there about that? I don't have the information to hand.

c) When citing an entry in a book, try not to use page numbers, as different printings may cause these to change between editions. Please refer to the section / chapter instead. See the existing examples for a sample of how this works. --prime mover 04:30, 20 November 2011 (CST)


 * Understood, thank you prime.mover. I had a feeling that something like this was the case, but I gave up trying to follow the conversation on the talk page, I felt it was way above my head. I'll see if I can find something, and I'll try the talk page again. --GFauxPas 07:11, 20 November 2011 (CST)


 * I was in over my head too. In fact, I'm fairly sure Qedetc was in over his head as well. Probably so far over his head you couldn't see the bubbles. --prime mover 07:21, 20 November 2011 (CST)


 * I want to add that I refuse to believe all of analytic geometry is based on the axiom of choice. --GFauxPas 08:36, 20 November 2011 (CST)

Sizing of Images
When you are creating images, there is no need to create different versions depending on what size you want it. All you do in the code is add " px" to tell the browser how many pixels (high? wide? Don't know) to render the image.

In order to keep the images folder tidy (it can't be organized easily) I will update the cone page to use File:ConeVolumeProof.png and size it appropriately, then delete File:ConeVolumeProof2.png.

--prime mover 04:45, 20 November 2011 (CST)

Trig integrals
Good work on all these trigonometric integrals. It's something I've been meaning to get round to doing but haven't done yet. We have the opportunity of providing the best repository of integrals on the internet. --prime mover 12:06, 24 November 2011 (CST)
 * My pleasure. I don't like proofs like the secant proof where the steps come out of nowhere, but it is what it is. Thanks for the compliment. --GFauxPas 12:09, 24 November 2011 (CST)
 * Understood, and I'll stick to x if you like x better, I apologize for wasting your time. As I said, I'm a slow learner at some things. I'm still trying to measure what needs to be said and what doesn't. --GFauxPas 14:06, 24 November 2011 (CST)
 * Okay, here's a general rule: if it's in place using notation you're not happy with, but it's sound, then leave well alone unless there's a good reason not to (e.g. it's incorrect). If you prefer using theta in the proofs you work on, fair enough, but if and when we expand the understanding to take on board complex numbers we might take the opportunity of amending the notation again. Of course, if it has a proofread and/or tidy template (or it's otherwise new by a contributor who has not yet assimilated the house style) then the above does not apply. Of course, if you really don't agree with the presentational style, raise the question in the discussion page. That's always an option. --prime mover 14:58, 24 November 2011 (CST)
 * Thank you for your patience with me, Prime.mover. I don't care what symbols I use, and if it makes you happy you can change any notation I use, I don't care. I just have accustomed myself to using theta for trig, I don't mind using x or whatever if you like it better. The main reason I edited the cosine page there was because the proof didn't address the sign of the sine. Also, can I leave it as a given that differentiation and integration are linear operators? I've been putting it in the proofs, but it's left implied in most of the proofs I see outside of PW. --GFauxPas 15:08, 24 November 2011 (CST)
 * I rarely bother to note the derivative of a minus, because it all follows with simple algebra anyway. If there's a specific need to invoke a complicated linear combination, then perhaps note that, but for a simple constant multiple I would not. Note the corollary to the derivative of the exponential which includes the drv. of $e^{cx}$ - you might want to add something similar as a corollary in the trig functions. In fact, drv of $\sin (ax + b) = a \cos (ax + b)$ is a really useful corollary, so when we get onto complicated substitutions in the messy integrations involving quadratics, you just need to invoke that page and it saves a lot of extra work on the substitution. --prime mover 16:26, 24 November 2011 (CST)

Certainly the integrals of tangent, secant etc. are worth adding, but would you like me to add pages for the integrals of functions like $\sec x \tan x$, $\sec^2 x$? --GFauxPas 13:40, 25 November 2011 (CST)
 * My rule of thumb is: a result is reported in a text book as worthwhile results then they can probably go in. Otherwise, if they're needed in the course of a more complicated proof then we could add them when they were needed. Otherwise I wouldn't bother. --prime mover 17:23, 25 November 2011 (CST)
 * It might be feasible to compute the indefinite integrals for $\cos^n x\sin^m x$ and $m,n\in\Z$. That page would be worthwhile I think as a reference table, and would cover all of these. --Lord_Farin 17:32, 25 November 2011 (CST)
 * That's one that's been on my own list to do in due course - but there's lots of other fiddly stuff I want to get sorted out while I have the particular books in front of me. Feel free to get there first ... --prime mover 17:44, 25 November 2011 (CST)

Grammatical note
Reinstating this section because its still relevant.

I see you starting lines with a capital letter where it does not need one. Here is an example:


 * The hyperbolic tangent function is defined on the complex numbers as:


 * $\tanh: X \to \C$:


 * $\displaystyle \tanh z := \dfrac {\sinh z}{\cosh z}$


 * Where $\sinh$ is the hyperbolic sine, $\cosh$ is the hyperbolic cosine, and $X = \{ z : z \in \C, \ \cosh z \ne 0 \}$."

The word "where" should not have a capital letter. The above is all (technically) one sentence, like:


 * "The best food is:
 * FISH AND CHIPS
 * where chips are made of deep-fried potato."

See? As "where" is part of the same sentence, it does not start with a capital letter.

I have been changing them consistently where I've seen them, hoping you'll pick it up by following examples, but now I see you changing one in the other direction, I have to mention it.

I understand that Microsoft make things complicated by automatically making the first letter after every new line / return start with a capital, but Microsoft are cracked.


 * Your comment in the edit page about "committed to memory", you might want to amend your subroutines to ensure it's your hard drive not your RAM it gets committed to, as I notice the same is being done on your sandbox page for Riemann Sum. --prime mover 00:19, 25 November 2011 (CST)