Recent content by ForMyThunder

Take the sets (R-Q)x{q} for rational q. This is a countable set of closed sets with nonempty interior but their union is the entire space. Hence, it isn't Baire.

(R-Q)XQ isn't Baire. To prove that look at "slices".

Yep. It's that simple.

The metric you have, the ##ds_{d+1}^2##, gives you the components of the metric, ##g_{ab}##, which you can just read off. Feeding this into the Christoffel symbols and the Killing equation gives a system of differential equations which you solve for ##X^a##. I think you've got this far. I think...

I believe the term "correspond" is causing the confusion. To me, this just means that there is some sort of mapping from one set to the other, in this case from the set of orthonormal bases at p to the set of locally inertial reference frames. It doesn't exactly give a definition; in his first...

Yes. What I get from reading the document, and I may be wrong in this, is that it is saying "given any point ##p\in M## and any orthonormal basis ##e_\mu\in T_p M##, there is an inertial coordinate system (that is, such that the Christoffel symbols are 0) such that the coordinate frame...

It's most likely a typo: should be eta and not g. This, ##g(e_\mu,e_\nu)=(e_\mu)^a(e_\nu)_a=g_{\mu\nu}##, is the definition of the components of ##g##, the ##g_{\mu\nu}##. The book "Gravitation" by Misner, Thorne and Wheeler gives the definition for local Lorentz frame as you have described...

I was just wondering if there are any written documents which give the views of the United States founding fathers' views towards separation of church and state. The constitution reads, "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof"...

If anyone has an amazon kindle, how does it handle math text, say from lecture notes. I've been told that you need to convert it from pdf. Does anyone know how it looks after it has been converted? Is it legible? What about textbooks that are in pdf format?

Say you got all the necessary vitamins and nutrients from pills at your local market. I was wondering if I could live off of these for an extended period of time. Obviously, I would need some sort of energy, so throw in spoonfuls of honey, sugar, or yogurt and I would also need to keep my...

So I've become aware that the more "good" choices we make, the easier it is to make a "bad" choice, e.g. if you're on a diet for a couple of months, its very easy to slip and have a piece of chocolate cake, that sort of thing. Here's the wikipedia. http://en.wikipedia.org/wiki/Ego_depletion So...

Homework Statement Set up the equations of motion for the system shown in Fig. 4.16. The relaxed lengths of the two springs are l1, l2 . Separate the problem into two problems, one involving the motion of the center of mass, and the other involving the "internal motion" described by the two...

This makes sense. When I go to log off, there's usually a popup that says something like "you need to kill this process" or "this process is still running" or whatever. I've just never paid any attention to it. I'll check up on it and ask any other questions if it doesn't work.

I don't know what's wrong with it. My antivirus doesn't detect anything and I built the think in February. It's Windows 7. It just started about a month ago but it does it occasionally and it has me worried. What could it be? When it freezes, I can still move the mouse around but it won't...

We still have a right to improve our own living conditions by getting a say in our government. America is the posterboy of "democracy" and it should be that the sentiment of the majority of its citizens should prevail no matter what class, profession, or background they come from.