Recent content by loopgrav

Get a copy of Hungerford's Abstract Algebra.

In my experience, by far the easiest editor to use (on a pc) is WinEdt. By default, it is configured to work with MiKTeX, and it couldn't be easier. See www.winedt.com.

Since I am new to this forum, would somebody please tell me how most of you post questions/replies with equations. Are you using LaTeX or some other equation editor? If it is LaTeX, do I simply incorporate an entire LaTeX file? Thanks for your help.

The Lie derivative is defined in terms of flows on a manifold. The fact that it is equal to the Lie bracket is a theorem that results from the definition. The most readable treatment I know of that doesn't get too bogged down in total rigour is Ted Frankel's "The Geometry of Physics." He also...

Pivoxa15: What HallsofIvy says is exactly correct. Just apply the definition (in a metric space) of open to see that ANY collection of open sets is open, and a FINITE intersection of open sets is also open. THIS IS ALL YOU KNOW FOR SURE (plus the fact that by definition the empty set and the...

I don't know what you mean by year 8. The only texts that I know of are college level and above. You may want to go to a nearby high school and talk to a math teacher if necessary to find a text. Alternatively, go to a nearby college bookstore and look at the course texts. If you wish, give me...

The cosmological constant was introduced to force a static solution to Einstein's field equations. Hubble made the empirical discovery that the universe is expanding, and the Hubble constant was originally defined as simply the experimental proportionality constant between the distance and...

Why are any of you continuing with this idiotic thread? Don't you have anything else to do? All of his questions have been answered repeatedly, and if nothing else I gave a detailed explanation along with several excellent texts that he could study on his own. In my opinion, this forum is to...

An arbitrary (ie possibly infinite) union is easily seen to be open, and it may very well also be closed (for example, if it is equal to the whole space under consideration), but that is irrelevant to this discussion. As to the closed sets [-n, n] for n=0, 1, 2, ... the intersection is {0}...

That's completely irrelevant to the issue. It still doesn't let you define force in a manner independently of other terms such as mass (constant or relativistic) or acceleration.

Look at chapters 2 and 3 of "The Fabric of the Cosmos" by Brian Greene. It is an excellent discussion of Newton's bucket and Mach's Principle.

This is actually a remarkably difficult question. In my opinion, the only term in Newton's second law F=ma that is even vaguely well-definined is the acceleration, and that assumes you believe Newton's "definition" of time. If you take the concept of force as well-defined, then mass is defined...

I just noticed this thread, and it seems really silly to me that it has gone on so long. So as a new observer, let me summarize what I think the essential points are from a fresh point of view. First of all, in any metric space (and hence in an arbitrary topological space) the union of an...

See "Quantum Mechanics in Hilbert Space" by Eduard Prugovecki. It's out of print, but you can find it at [PLAIN]www.campusi.com[/URL]. As stated above, the results for infinite-dimensional spaces are far more difficult than for finite-dimensional spaces, and as far as I know, most of the...

Here is proof. I had to edit somewhat because some of the mathematical symbols wouldn't copy into this window. You should be able to understand however. If you would like, I could email you the entire section in pdf form. (It's on polynomials over finite fields.) Theorem 6.20 Every finite...