Dave

Unless I'm mistaken, this is the change of base formula. Multiply through to get: logax logb a = logb x. Now suppose: u = logax => au = x (1) v = logba => bv = a (2) w = logbx => bw = x (3) (1) and (3) together imply that: au = bw. (2) implies that: au = (bv)u = bv.u So we must have bv.u = bw => vu = w Hence we are done.

You'll very much be able to see the beam if there are enough particles in the air and the lights are turned down. We just had a lecture in which the very same happened.

Unfortunately, I don't think there's a way around it. However, I'm probably not the best one to ask - not done this for a while

The one thing that I perhaps should have stated (skipped my mind earlier) is that A = {a,b,c} => |A| = 3 if a, b and c are all distinct elements.

I missed this a couple of days ago. Basically, there's a bug in the code atm. When your post gets converted back into html for the wysiwyg editor, it also converts the generated latex image into html instead of just displaying it as [math] [ /math] like it normally would. It's fixed in the latest version; I'll get it uploaded soon, although we're undergoing some changes atm, so it may be a few days yet.

It's a system that's been set up so that people who are experts in their field and contribute a lot to the forums can be given some kind of recognition. We literally created the usergroup today - there'll probably be an announcement about it at some point. We still need to announce the warning system properly as well.

Erm... not that I'm aware of. Everything I have seen or read has always infered that if A = {a,b,c} then |A| = 3.

I wouldn't know to be honest - it could be a number of things: 1) The hard drive is failing is one option and probably the most likely. If it starts to make strange noises, you might have a problem. 2) There's some kind of problem with the caddy that the harddrive is housed in (USB/Firewire might be on the blink, power supply up the shoot, etc). 3) Some kind of filesystem problem; quite unlikely since NTFS is usually pretty good and pretty much rock solid. 4) Your motherboard might have a problem. Unlikely at best. 5) OS/software issues: You might have some kind of malicious software on there. Something might be borked somewhere. I don't really know My suggestion is to take it out and test it on another computer. If you're still getting the same kind of problems, you can pretty much rule out everything except hardware failure. If this is the case, then try and get as much data off of it as you can and get it replaced. If the data is very important, then you might want to take it to a professional firm/data recovery place and see if they can get it off for you.

Indeed. That's why I said the question might help (that condition might be in the question )

I felt I needed to add something to the previous post. Let's assume we have some statement that we want to prove, and its dependent upon some number n - for example, your triangle number problem. We want to prove that 1 + ... + n = n(n+1)/2. To prove something by induction, we need to do the following things: 1) Prove it for n = n0, where n0 is just some "starting" value. 2) Assuming that it's true for some other number k, prove it for k+1. Then the statement is true for all numbers greater than or equal to n0. You can use the rest of uncool's proof to complete the rest.

My suggestion for your links and images (if you're still working on it) is to use preg_replace. You need to learn regexps for this thing - they're extremely quick, and extremely powerful. I'm afraid I'm not very good at them, but I could probably give you some hints (maybe).

When you delete a file, that file is not actually physically removed from the drive. Rather, the data blocks it occupied are marked as not in use - the data is still there, but the drive doesn't really care. It just knows that piece of the drive is available for writing. Then when you do some kind of write operation (copying a file for example), the drive will just overwrite those pieces when it gets to them. The "undelete" type programs will basically scan the empty sectors of the disc in order to find any files (or file fragments) that can then be restored. However, the chances of undeleting the files will decrease rather rapidly depending upon how much time has passed. If you leave the drive for longer, chances are that it would probably be overwritten. It also depends to a certain extent on how big your drive is. Added to this is the fact you've reformatted. If you chose the "quick format" option, then you might stand a chance. However, a "low-level" format will erase all of the data from the drive before it puts a filesystem/partition table on there, so you won't stand a chance of getting anything back from the drive. However, because you've reformatted, you probably won't get anything back from the drive now anyway. You can always try Good luck.

It would help if you posted the original question

Unfortunately I don't do Lie Algebras until next year. However, I've moved this to Modern/Abstract Algebra, since that's probably the best place for it

We're having problems with the off-site hosting. I'll talk to blike about it.

Unfortunately it appears that we're having problems with the off-site latex. Should be up soon, hopefully.

If you think that's something, try out Orbiter - it's a free (but closed source) space flight simulator. You can fly the shuttle, as well as quite a few other more space-age experimental craft. It's rather cool, but it's not easy to learn how to get these things into space.

I had this discussion with my old maths teacher quite a few years back. I believe the primary reason for choosing 360 as the number of degrees was as matt said - lots and lots of numbers divide it, making life a little easier when you're working with geometric shapes. The French did indeed create the grad unit of measurement. At the time of the French revolution, they tried to metricise everything - including time. Hence, 100 grads in a right angle. Unfortunately, it didn't really seem to catch on (except in some areas of engineering, I believe).

Well, neuroscience is a rather different field from nanotechnology.

I have a P4P800-E (an older version of the one mentioned above). Those settings are what I use for both XP and linux. You should note that if you don't have have enhanced mode support enabled, then it will most likely disable one of the SATA ports and one of the IDE ports. Check the manual for the motherboard, since it varies. Enhanced mode is only supported by 2000/XP, but you shouldn't have a problem there.

Have you tried something like nasm? I think that has a 32-bit build available. Plus lots of documentation, although I think that's more to do with the assembler itself, and not the language.

Although I am an avid Mac supporter, I'm not entirely sure that's true. From my experience, games play quite a bit faster on XP than OS X, although I haven't tried for the past couple of years.

Actually, the thing you call "obverse" is the contrapositive of a logical statement. I've never heard the word inverse used in these terms though.

Say what now? Math definition of what, precisely?

It's the equation for the triangle numbers, and is given by: [math]T_n = \frac{n(n+1)}{2}[/math].