the tree

I'm fairly sure that the L stands for Lie as in Lie-algebras and Lie-groups. I have a vague understanding of what those are. So urm... that's the closest I have to a clue, and I could be wrong.

The only time that is guaranteed to work is for a continuously differentiable, strictly monotonic function. If a function is not injective, then it does not have an inverse function so the derivative cannot be found.

You're stumbling around in circles here. You're acknowledging the existence of the other three fundamental forces, then claiming that magnetism is the underlying characteristic of everything? To be clear, the four fundamental forces behave in entirely different ways. That doesn't mean they don't have a "common cause" or something like that, but you'd have to explain how one factor could be manifested in four different ways.

Eurovision is traditionally awful, kind of a long running joke, most artists wouldn't risk going on it. Don't let it influence your view on European music.

You should be integrating [imath]k x[/imath], not [imath]k[/imath]. Hence being out by a factor of [imath]x[/imath].

Please, when using quotations and extracts like that, give credit. Usually just as a [source] or similar. All materials are magnetic - that is certainly true. That particular article is using material interchangeably with matter which is acceptable but you should understand that it's not talking about matter on every 'level'.

Yeah, sorry, what? Magnetism is a thing that well, gets discussed in detail all the time. It's kind of complicated on some levels and really important on many. There aren't many dirty words in physics for that matter. Then you need some predictions, some data, some comparison with existing theory and eventually some sort of hypothesis. Well, one of four backbones by standard theory - but okay. Out of your league doesn't begin to cover it. But that's a good thing, you can only learn so much without the help of people a lot more experienced than you. Not really amongst any elementary particles.

In that context, that some term is equal to what is over the underbrace. Often they are used for general notes.

Yes and no. For elementary particles that are nearly always considered point particles - there is no evidence to suggest that they do (or, afaik, don't) have spatial dimensions. I think you missed Mr Skeptic's point there, you cannot know exactly where your particle is.

Quite a few, school here is mandatory up to the age of 16 - but I'm not sure how much good that does anyone.

Isn't that exactly what school is? Barely anything you learn is directly applicable to any specific task but it's generally considered important.

I don't think the toolbox analogy really holds, tools have really obvious purposes whereas it's not always apparent when you're gaining knowledge, what you're going to use it for. Unless you're actually reading an instruction manual, but that's a special case.

Seriously? People still use Google calculator for these things? http://www.wolframalpha.com/input/?i=convert+5424+to+binary

A theory produces testable predictions. A cube has 6 sides. And (-1)x(-1)=1.

Pot, meet Kettle. I think you two should get along. You people always like each other, right?

Occam's Razor takes down Last-Tuesdayism fairly neatly, the spontaneous creation of a convincing impression of age is one whole layer more complex than actual age.

(N.B. Not being American, I understand if everything I say is automatically dismissed) "as originally intended" doesn't sound workable to me. For instance, if the question was whether people's "right to bare arms" should be limited to exclude rocket launchers: the right to bare arms doesn't place any explicit limitation on what "arms" actually means because at the time lots of weapons that exist today just hadn't been thought of - there is no original intent. If the text doesn't give a really obvious answer, and having been written hundreds of years ago that's understandable, then that should be fixed. When the text does give a really obvious answer then that should be stuck to - that's why laws are committed to writing in the first place.

Very much this. Teaching old dogs new tricks is too much of a challenge in the first place to test whether you actually understand something. Whether you could explain it to a child would be a better test. There are, however thing that I understand and could explain but it'd take a while. Lots of things worth learning really cannot be summarised in less than an hour. (my grandmother could probably explain a little bit of chemistry to me - she worked for some government thing for poison control or something)

Retro is not always cool.

I think the other people in the library are actually getting annoyed by my stifled laughter so I really am going to go home and to bed now. ANYWAY Squares are two dimensional, they expand over any two orthogonal axes. Orientation is arbitrary. Now it's a long walk home and I need a cigarette, so goodnight.

2. It needn't bend at all. Not if you rotate it quarter of a radian. KEYWORDS

Roughly: Taking not(x=0 and x=1) as given, ( (x>0 and x=1) or ( x=0 and x=1) ) and not(x=0 and x=1) => (x>0 and x=1) by disjunctive syllogism.

What is a Google?

^-

I'm tempted to say cast it aside as degenerate. More formally, demonstrate that the first three cases are the only ones that can actually exist.