Tom Mattson

By any chance, is this challenge a school assignment? If so then I think that you should post your own thoughts on the matter.

I don't get it. AD and BC are both in the loop. If you apply the right hand rule to the loop' date=' then you are applying it to every segment, BC included. It's not true for either shape. You do get an induced current in both cases because the magnetic flux through the loop varies with time.

Can't you see that your premise and your conclusion say exactly the same thing?? I beseech the powers that be to lock this thread. It has descended into sheer crackpot nonsense.

No' date=' not at all. In fact I'm more amused than anything else. You are posting on a message board that is devoted to science. That means that you can expect to have your mistakes pointed out, and you can further expect suggestions on how to remedy them. Mathematics is an academic discipline that requires a great deal of hard work and dedication. There are people here who have done that hard work. When you post things that contradict what every authority in mathematics says about mathematics it sends the message that you think you know the subject better than they do, despite the fact that you clearly have not done the necessary hard work to understand it.

And the point I am trying to explain is that your goofball notions of mathematics are rejected by those who work in the field.

That doesn't answer my question. Mathematics is an a priori discipline. All mathematical theorems follow from mathematical definitions by mathematical rules of inference. The physical universe plays no role in deciding mathematical truths, apart from the fact that material brains are needed to carry out the thought processes.

It is faulty' date=' for that very reason. It is clear that [imath']0.999 \neq 1[/imath]. Also, why bother to bring up physical systems or quantum fluctuations? They have nothing whatsoever to do with determining a mathematical truth.

That's true of every equation of physics.

No, in the end you have f(x,y,z).

I can't tell what you're asking.

String theory does have equations. Go to this page and search for titles containing the words "introduction string theory".

Speaking for myself: I don't picture it at all. I adopt the so-called "shut up and calculate" view of quantum mechanics. That wave/particle duality thing is just a descriptive term used to present QM to novices anyway. If you look at the theory itself' date=' there is no dual description of the mechanics of particles. edited to add: PS, the wave/particle duality has nothing to do with E=mc[sup']2[/sup]. The former notion comes from quantum theory, while the latter comes from relativity.

You can't get it from what was given. You have to have a reaction in which water is a product.

You leave them out of it. If [imath]\vec{\nabla}G=\vec{f}[/imath] then: [math]\frac{\partial G}{\partial x}=f_x[/math] [math]\frac{\partial G}{\partial y}=f_y[/math] [math]\frac{\partial G}{\partial y}=f_z[/math]

Certainly not. Look at the equation of the ellipse: [math]9x^2+4y^2=36[/math] Put it in standard form (do this by dividing by 36): [math]\frac{x^2}{4}+\frac{y^2}{9}=1[/math] [math]\frac{x^2}{2^2}+\frac{y^2}{3^2}=1[/math] As you can see from this equation' date=' the [b']highest[/b] point on the ellipse has a y-coordinate of 3. So y=6 is quite out of the question.

You shouldn't be trying that at all. When the problem states that the y-intercept of the tangent line is at [imath](0' date='6)[/imath'], you are not being told that [imath]y=6[/imath] is in the range of the ellipse. You don't know where the tangent line intersects the ellipse, so call the point something like [imath](x_0,y_0)[/imath]. From there you can find the slope of the line in terms of the unknown point.

I do listen exclusively to CDs at this point, but I swear I will never send or receive a 'text message'. Computers are for email, telephones are for talking, and ne'er the twain shall meet.

Yep. Didn't Aretha Franklin have a song about this? Oh yeah' date=' [i']"Chain chain chain, the chain ruuuuule."[/i] Ba-dum-bump. Seriously, you can think of csc2(x) as [csc(x)]2, and then use the chain rule. Yep. You need the product rule this time, and you'll need to apply it to each term in f'(x).

I think you missed my point. Yes the rule you state is true. No it is not a "first principle" (as the limit definition of f'(x) is). No you can't use it when asked to differentiate something from first principles.

You aren't talking about relativity' date=' you're talking about relativISM. There's a huge difference (pun intended). It's a philosophical school of thought that has been discussed for hundreds of years. And yes, the paradox "There are no absolute truths" is very well known, and there exists a great deal of literature on the subject. You get it rolling. You're the one who started the thread, so present an argument against relativism. It's your dime, start talking.

Are you trying to say the following? [math]\left\{f:\mathbb{R}\rightarrow\mathbb{R}\mid\frac{df}{dx}+2f=1\right\}[/math] If so then you are correct. [imath]f\equiv0[/imath] doesn't satisfy the condition specified in the set definition. Type the following, without the spaces: [ math ]\mathbb{R}[ \math ]

No' date=' 2/2 is exactly 1. No, 0.001 is not a real number.

There's no way that you or anyone else could possibly reach any sensible mathematical conclusion without falling back on mathematical proof, and proofs that establish the truth of the statement 0.999...=1 abound both in textbooks and on the internet.

Yeah' date=' but you can take it a lot further than you've taken it so far. This forum even has LaTeX typesetting so that you can make yourself crystal clear. Well, instead of using your online time merely alluding to your ideas, perhaps that time might be better spent actually exposing them, yes?