Dave

I imagine the betting companies would lose quite a lot of money. Compared to their takings from sports bets etc though, I don't think they'd be in serious trouble, and even if they were, I wouldn't care too much.

Just get some books and read up on it It's not too hard to understand the basic principles.

I don't think the betting companies have to worry about going broke tbh. All the rovers have shown is that Mars once had a wet climate, not that the planet supported life.

Quoted from BBC News: "The Universe is at least 156 billion light-years wide, say astronomers. The estimate comes from data obtained by a space probe that is examining the so-called Cosmic Background Radiation - often called the echo of the Big Bang. The echo contains information of what the cosmos was like when it was young and how it might develop. The cosmos is 13.7bn years old but the stretching of space with its expansion after the Big Bang means that simple distance measurements do not apply." For more information, look at: http://news.bbc.co.uk/1/hi/sci/tech/3753115.stm

We don't have the technology to clone people safely yet - we can hardly manage it with sheep. However, that's beside the point. What you're saying is that we should grow a clone and (effectively) kill them to get the face skin. There's a couple problems with this: 1) It's horribly unethical and immoral. 2) The clone will grow at the same rate as the person who wants the transplant; hence it would be years before the procedure could take place. What I was talking about was growing a selected part of the body (in the same way as producing organs) - effectively I was talking about growing a new face at an accelerated rate, which is beyond our means. In order for your method to work, you'd have to grow clones (which would be sentient beings) in order to harvest organs; this is an area of great ethical debate, and is one of the reasons why scientists are so touchy about human cloning.

I'd assume it's harder to breathe when it's colder (e.g. Antarctica, etc), but I don't think it has much to do with the physical properties of oxygen; more to do with the temperature of the air (i.e. it's cold).

(please note: mimeTeX is now redundant, we're now using LaTeX, refer to t'other tutorial).

Liquid Oxygen boils at about -183.0 degrees C, which is about 90K.

This is a short guide to using the new LaTeX system that has been implemented on the boards. First off, for those who don't know what LaTeX is, a short description. LaTeX is, to all intents and purposes, a fully fledged math typesetting system - basically put, you can write math with it. It's a very flexible and hence very advanced piece of software, and the syntax for it is quite complex, but fairly easy to learn for typesetting smaller equations. On scienceforums.net, we've implemented a small LaTeX system to allow you to typeset equations (in other words, cut out all the x^2 stuff and make things easier to read for everyone). The basic principle behind it is this: you have a LaTeX string, and you surround it by [math][/math] tags. I'll come to the syntax of the actual string in a moment. For those who can already use LaTeX (and indeed, those who can't), a few things to note. In the system we've implemented, a tex file is created, surrounding the string you input with a \begin{display} environment so there is no need for $, $, \[ etc. Also note that we've included the standard AMS files for you; if anyone wants any special characters, I'm sure we can probably accommodate your needs. The images are clickable, so you can see the code that was used to make them by clicking. Now that's all out of the way, onto some examples Examples [math]x^2_1[/math] - Indexes (both subscript and superscript) on variables [math]f(x) = \sin(x)[/math] - A simple function. [math]\frac{dy}{dxx} = \frac{1}{1+x^2}[/math] - Example of fractions - you can create small fractions by using \tfrac. [math]\int_{-\infty}^{\infty} e^{-x^2} = \sqrt{\pi}[/math] - A nice integral. [math]\mathcal{F}_{x} [\sin(2\pi k_0 x)](k) = \int_{-\infty}^{\infty} e^{-2\pi ikx} \left( \frac{e^{2\pi ik_{0}x} - e^{-2\pi ik_{0}x}}{2i} \right)\, dx[/math] - a Fourier Transformation, which is rather large. I could go on and on, but I'll go onto explain some of the basic syntax of LaTeX. Syntax Functions & General Syntax Basically put, if you want to write a math equation in LaTeX, you just write it. If you wanted f(x) = 3, then bung that between to math tags and you're done, producing [math]f(x)=3[/math]. Don't worry about extra spaces or carriage returns, because in general LaTeX will ignore them. It does get a little more complex than this, but don't worry about that for now. Remember that any letters you type in will be presumed to be some kind of variable and hence will be italicised. We also have functions to display more complex things like matrices and fractions, and they have the syntax of having a \ before them, usually followed by some kind of argument. For example, \sin will produce the function sin and \frac{num}{denom} will produce a fraction with a specified numerator and denominator. More on these later. Also remember that LaTeX is case sensitive, so \sigma is NOT the same as \Sigma. Subscripts and Superscripts This is perhaps one of the easiest things to do in LaTeX, and one of the most useful. Let's, for the sake of argument, say you wanted to write x2. Then you'd write x^{2}, producing [math]x^2[/math]. Notice that you don't necessarily need the { and } in cases where you only have 1 thing in the index, for example x^2. But it does care if you want to write something like [math]x^{3x+2}[/math]. Subscripts are done similarly, but you use the _ operator instead of ^. If you want both subscript and superscript, then use the syntax x^{2}_{1} - which is equivalent to x_{1}^{2}. Fractions and functions As I've mentioned, fractions are generated by using the function \frac{num}{denom}. For example: [math]\frac{1}{3}[/math] [math]\frac{7}{x^2}[/math] If you want smaller fractions, you can use \tfrac, to produce things like [math]\tfrac{1}{2}[/math] which will fit into a line nicely without having to seperate it. LaTeX has some nice in-built functions like \sin, \cos, etc. I'm not going to write them all down here, but I'll point you to a website at the end of the document that contains them. Likewise, you can write symbols (such as infinity by using \infty) and Greek letters (e.g. \phi, \Sigma, \sigma, etc) Bracketing You can get all your usual brackets just by typing them straight in; for instance, (, |, [, etc. However, sometimes they won't be the right size, especially if you want to write something like (1/2)n. You can get around this by using the \left and \right commands, and then placing your favourite brackets after them. For instance, to write (1/2)n, we have: [math]\left( \frac{1}{2} \right)^{n}[/math] Integrals, Summations and Limits Integrals can be produced by using \int, summations by \sum and limits by \lim. You can put limits on them all in the right places by using the normal subscript/superscript commands. For instance: [math]\int_a^b x^2 \,dx[/math] [math]\lim_{n\to\infty} \frac{1}{n} = 0[/math] [math]\sum_{n=1}^{\infty}\frac{1}{n^2} = \frac{\pi^2}{6}.[/math] Summary There's a lot more things you can do with LaTeX, and I'll try to add to this as time goes by. Have a look at: http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/'>http://www.maths.tcd...ns/LaTeXPrimer/ - the LaTeX primer http://omega.albany.edu:8008/Symbols.html'>http://omega.albany....08/Symbols.html - some symbols that you might find useful. If you have any questions about the system, send me a PM and I'll try to help Cheers.

What?

No, Taylor's theorem is defined over a closed interval (i.e. [math]f:[a,b] \to \mathbb{R}[/math]) and over a finite number of terms and has a remainder at the end of it: i.e. [math]\exists\, c \in [a,b] \mbox{ such that } f(b) = \sum_{i=0}^{n} \frac{f^{(i)}(a)}{i!} + \frac{(b-a)^{n+1}}{(n+1)!} f^{(n+1)}© [/math] Or at least, that's the version I have.

No, Tesseract is going along with it. That's a completely different story

Here's the page from MathWorld (which is like a shrine to Mathematics ): http://mathworld.wolfram.com/FourierSeries.html

There's a nice Mandelbrot set one going around, although I don't have an URL for it. Fractal ones are usually quite nice

(for anyone that's wondering, it's basically Maclaurin's theorem).

I have to say, I'm stumped. I've tried solving this problem but it's being a complete gimp and I'm completely fed up with it. Here it is in all its glory: Use Taylor's theorem to prove that the function [math]f:\mathbb{R} \to \mathbb{R}[/math] given by [math]f(x) = e^{ax}\cos(bx+c)[/math] (for [math]a, b, c \in \mathbb{R}[/math]) can be written as the power series [math]f(x) = f(0) + f'(0) x + \cdots + \tfrac{1}{n!} f^{(n)}(0) x^n + \cdots[/math] for all [math]x\in\mathbb{R}[/math]. Any help is much appreciated as the question is worth 14 marks/25 in a past paper

You probably won't get this unless you're from the UK, but nevermind: 2 Scousers are riding along the M62 from Manchester to Liverpool on a motorbike. They break down and start hitching a lift. A friendly trucker stops to see if he can help and the scousers ask him for a lift. He tells them he has no room in the wagon as he is carrying 20,000 bowling balls but will take a look at the bike for them. He tries everything he knows but is unable to repair it. Time is getting on now and he's late for his delivery so he tells the scousers he has to leave. "R hey lad" they say "gissa lift". The trucker once again explains that he has no room as he is carrying 20,000 bowling balls. The scousers put it to the driver that if they can manage to fit in the back will he take them and he agrees. They manage to squeeze themselves and their motorbike into the back of the wagon so the driver shuts the doors and gets off on his way. By this time he is really late and so puts his foot down. Sure enough PC Plod of Greater Manchester Police pulls him up for speeding. The good officer asks the driver what he is carrying to which he replies Scouse Eggs. The policeman obviously doesn't believe this so wants to take a look. He opens the back door and quickly shuts it and locks it. He gets onto his radio and calls for immediate backup from as many officers as possible. The dispatcher asks what emergency he has that requires so many officers. "I've got a wagon with 20,000 Scouse eggs in it - 2 have already hatched and the b*****ds have managed to nick a motorbike already".

It is rather tedious at times, although it's necessary so that people can decide more easily as to what they want to do with their future. This is straying off-topic quite nicely, should probably get it back on topic before someone comes and lynches me (well done on the 1000th post btw)

Yes, you're right. Was thinking of something else

Sorry if I'm being ignorant, but what's that all about?

I dunno, it might have some use as part of a giant wok.

Or perhaps the robots gained intelligence and tried to kill us? (he probably fell down some stairs or something )

ouch. that hurt. Btw, anyone seen Face Off? It's all about face transplants (only stupidly unscientific)?