Dave

Gah, not in this part of the UK. It's been foggy and horrible all day now - no let up at all.

Moved to Applied Mathematics.

From the second equation, you must have [imath]d(e+f) + ef = B[/imath]. Then use the first equation and send equation to get [imath]d(A-d) + \frac{C}{d} = D[/imath]. This isn't a simple equation. In fact it's a cubic, and you'll have a hard time finding the roots from the looks of things If you're interested in solving cubics, you'd be better off looking at Cardano's method (just google for it).

You may have noticed the new "Speculations" forum at the bottom of the page. It should be fairly obvious to you all as to what that forum is all about, but I'll state it just to be sure. There have been lots and lots of speculative theories posted in the Physics section of the forums. For the most part, these are completely and utterly wrong, and generally it annoys a lot of people. So, to alleviate the pressure, this forum has been created for people who want to post theories that have little or no base in scientific knowledge. If you want to post a new theory, or indeed respond to an existing one, then please read the rules of the forum. In particular, note that if you're going to ignore all of the responses to your thread that criticise the theory posted therein, then you will be warned and the thread will almost certainly be closed. If you do this often enough, then you are obviously going to be banned. Also, please note that any thread of this nature posted elsewhere in the forums will be moved to the Speculations forum without your consent. So please make sure to post in the correct forum. Thanks.

What is this forum for? There have been lots and lots of speculative theories posted in the Physics section of the forums. For the most part, these are completely and utterly wrong, and generally it annoys a lot of people. So, to alleviate the pressure, this forum has been created for people who want to post theories that have little or no base in scientific knowledge. Hopefully members of the community will be kind enough to provide some form of peer review on the ideas. Rules of the forum Please be civil, and try to get along with one another. Have some respect for everybody's ideas, no matter how wrong you may think they are. Threads will be closed and/or deleted if you provide no evidence to back up ideas that you post here. Moderators can and will enforce these rules if not followed. Of course, the usual SFN forum policy applies here. Feedback is always appreciated. If you see a post that worries you, then please use the "Report Post" feature as usual. Other than that, send a PM to a staff member, and we'll try and help you as much as possible.

It also depends on what you intend to use it for. Linux is still quite lacking in some areas (the most prominent being games). Personally I find myself going to Linux for a few days then switching back to XP after a few days.

That's no problem I thought the integral test would be rather like breaking a nut with a sledgehammer for something as simple as the Harmonic Series. Plus I think this way of proving it is quite nice.

The proof is fairly straight-forward. You need to take careful note of the following grouping: [math]H = 1 + \underbrace{\frac{1}{2}}_{\geq \frac{1}{2}} + \underbrace{\frac{1}{3} + \frac{1}{4}}_{\geq \frac{1}{2}} + \underbrace{\frac{1}{5} + \frac{1}{6} + \frac{1}{7} + \frac{1}{8}}_{\geq \frac{1}{2}} + \underbrace{\frac{1}{9} + \frac{1}{10} + \frac{1}{11} + \frac{1}{12} + \frac{1}{13} + \frac{1}{14} + \frac{1}{15} + \frac{1}{16}}_{\geq \frac{1}{2}} \cdots[/math] From this, you should be able to see that if [math]s_n = \sum_{k=1}^n \frac{1}{k}[/math], then [imath]s_{2n} \geq s_n + \frac{1}{2}[/imath]. You can also prove this: [math]s_{2n} = s_n + \sum_{k=n+1}^{2n} \frac{1}{k} \geq s_n + n\frac{1}{2n} = s_n + \frac{1}{2}[/math]. Now it's easy to prove that [imath]s_{2^n} \geq 1 + \frac{n}{2}[/imath], since [imath]s_{2^{n+1}} = s_{2\cdot2^n} \geq s_{2^n} + \frac{1}{2} \geq 1 + \frac{n+1}{2}[/imath] by induction. All you have to do now is say that you've found a subsequence [imath]s_{2^n} \to \infty[/imath] as [imath]n\to\infty[/imath], and since [imath]s_n[/imath] is a strictly increasing sequence this means that [imath]s_n\to\infty[/imath]. Hence the Harmonic series diverges.

It's unfair, but unfortunately that's the way it seems to go these days. However, with the proper legal aid (and assuming the disclaimers were in place) I would think your friend might get away with it. That being said, I don't know enough about the law in this instance to offer some concrete advice. However, it underlines why we don't allow that sort of posting on SFN. We can get in serious trouble as well as you guys, so please bear that in mind before making posts on the subject.

We're currently having a number of server issues (you might have noticed the slowness). I'm looking into the problem at the moment, and hopefully I'll be able to get back and give you all some answers fairly soon. Until then, I can only apologise for the slow response when posting and general browsing. Hopefully this should start to pick up in the next 3-4 hours.

I suspect for making posts much like this one.

Use a binomial expansion for [imath](1+x)^{\frac{1}{2}}[/imath]. Since this converges for |x| < 1, you can happily slap in x = -0.1, work out the first 4 terms of the series and get a pretty accurate answer.

I'm fairly sure you're talking about projective 2 or 3-space, but I can't remember which. I do remember that if you squash the boundary of a Mobius strip to a point, you get P2. Can't remember the defining equation though.

Well, the idea is to manipulate the limit to get the answer. He's trying to derive the ideas of differentiation from first principles, so doesn't necessarily know anything about the derivative

That's your own opinion, and fair enough. But that's no reason to continually slate it, guys. It was originally posted as a nice little remark. Clearly there are numerous ways to prove this statement that are much more concise and don't appeal to some big and horrible theorem about such and such. The point is that it is clearly not a practical proof. It's one of those neat tricks that you converse about in a civilised fashion, and I'm not entirely sure why it's drawing so much criticism. Moreover, this is the second time I've made such a comment on this thread - what is the big deal about this? Frankly, after a few weeks of proving one monotonous theorem after the next, I think something like this is a little breath of fresh air. Ease up a bit, guys.

Unfortunately vB doesn't have anything to do wit hthe server speed. Mainly it's the amount of hits the server is getting, and I can't really touch the config because it would break quite a lot of cPanel functionality. But yes, a dedicated server would likely fix the speed issues. However, they're quite expensive and blike's busy with med school, so I don't know what'll happen for the time being.

No, it had nothing to do with copyright stuff. Basically it got borked after a server upgrade, and blike's not keen on it coming back. Hence, it probably won't be back for quite some time, if ever.

Sorry, I hadn't noticed your post until a few minutes ago I'm looking at ways of enabling people to draw diagrams on here with something like pstricks or similar. If you find any LaTeX packages that you think would be useful, then please let me know.

Sounds like you have some bad blocks on your disk. Tried running a disk scanner/repairer?

You can estimate it. Consider that one keystroke will take up precisely 1 byte, and say that the average typing rate is about 35 wpm (quite fast). The average word in the English language is about 5.7 characters in length (can't remember where I got this one, but it's about reasonable). So if you were to type 35 wpm you'd be consuming about 200 characters per minute which translates to 200 bytes/min. So, if you had a 512mb flash drive onto which you stored the information, then you'd be able to log everything a person typed into a computer for the next 2.68 million seconds - roughly equivalent to 745 hours or 31 days. And that's if the person was typing continuously for that amount of time The answer is: quite a lot

The main reason for me is that calculus is needed in pretty much every branch of physics. It's a subject that really does have a finger in most pies

Yeah, sorry for all of this downtime. I think some of it might be to do with the fact that our hosts are currently upgrading and migrating their servers over to a new data centre, and that's caused a few problems. Hopefully, it should all be sorted out now, but I guess we'll wait and see.

I've closed the thread, since it's gone on far too long now.

ZA is a funny beast. I use the free version for the lovely firewall - I find the other stuff pretty pointless.

Just because k is a constant doesn't mean it's unitless. For example, take Newton's law of universal gravitation: [math]F = -\frac{G m_1 m_2}{r^2}[/math]. G is certainly a constant (the gravitation constant) and it also has units N m2 kg-2 (you can work this out).