.999~ = or != 1

[Durandal]

Oh so that's what you're doing. I'd long since forgotten about the Hell that was integration by parts.

Personally, I dislike that u,v,du,dv formulation. Yes, it is prima facie more general, but only at first glance--but if I think of integration by parts as simply the integral of the product rule (fg)' = f'g + fg', then everything comes out easier.

It's not so much the notation that infuriates me; it's that if you choose the wrong substitutions, you can wind up spending a half hour to find out that you did so.

[Kuroneko]

It's not so much the notation that infuriates me; it's that if you choose the wrong substitutions, you can wind up spending a half hour to find out that you did so.

That's not bad. What's bad is when you do half an hour of substitutions with no result, because integration by parts does not apply at all in any manner whatsoever.

Try this: I = \int_0^{\pi/2}\log\sin(x) dx.

[Andrew J.]

If this keeps up, I'm posting the reason why the population of the universe is zero.

I'll save you the trouble.

The universe has infinite space, but the space occupied by people is finite. Since any finite number divided by infinity is as close to zero as makes no odds, the average poplation of the universe is zero.

[El Moose Monstero]

If this keeps up, I'm posting the reason why the population of the universe is zero.

I'll save you the trouble.

The universe has infinite space, but the space occupied by people is finite. Since any finite number divided by infinity is as close to zero as makes no odds, the average poplation of the universe is zero.

Thank you, Douglas Adams... (or at least, that's where I first read it)

[Specialist]

The universe has infinite space, but the space occupied by people is finite. Since any finite number divided by infinity is as close to zero as makes no odds, the average poplation of the universe is zero.

I thought it was already proven the universe is expanding, therefore it's not infinite in size.

[Durandal]

The universe has infinite space, but the space occupied by people is finite. Since any finite number divided by infinity is as close to zero as makes no odds, the average poplation of the universe is zero.

I thought it was already proven the universe is expanding, therefore it's not infinite in size.

It is infinitely expanding. But you're thinking of the universe as a giant bubble or something similar, which is not the case. The universe's boundaries are not expanding, because the universe has no boundaries, since it has no center. What is expanding is space-time. It's more like stretching an infinitely elastic sheet than a balloon made of infinitely elastic material blowing up.

[Mad]

The universe has infinite space, but the space occupied by people is finite. Since any finite number divided by infinity is as close to zero as makes no odds, the average poplation of the universe is zero.

Zero per infinitely-large volume. Leaving out units is bad.

[Durandal]

It's not so much the notation that infuriates me; it's that if you choose the wrong substitutions, you can wind up spending a half hour to find out that you did so.

That's not bad. What's bad is when you do half an hour of substitutions with no result, because integration by parts does not apply at all in any manner whatsoever.

Try this: I = \int_0^{\pi/2}\log\sin(x) dx.

Heh, I always figured that I'd never have any use for it at all.

[muse]

student: why do we have to learn all this stupid integration and identities and stuff?

teacher: because one day some guy on a message board will ask you to prove that 1=1, and if you don't know how you'll look stupid.


It's scary how fast one can forget this stuff, a year ago I could do the proofs and stuff for these equations, now I can't even remember what the hell it all means. This is why I'm not in engineering or sciences.

[AnimeJet]

student: why do we have to learn all this stupid integration and identities and stuff?

teacher: because one day some guy on a message board will ask you to prove that 1=1, and if you don't know how you'll look stupid.

HA! XD

It's scary how fast one can forget this stuff, a year ago I could do the proofs and stuff for these equations, now I can't even remember what the hell it all means. This is why I'm not in engineering or sciences.

Its 'cause you never need to use this stuff anyway(unless you go into a career that needs it..).. english however...

[phongn]

Can someone post the LaTeX code to that expression? I'd like to print it out

[kojikun]

someone should code something into phpBB that allows you to display mathematical notation. I'm sure I could figure out some way, but then, I am not the person at phpBB.

[phongn]

It'd be a PITA to do that. Our best bet is MathML, but support for that is very small.

[Durandal]

Can someone post the LaTeX code to that expression? I'd like to print it out

Here's mine if you'd like it.

Code: Select all

\documentclass[11pt]{article}
\begin{document}

\begin{eqnarray*}
\left|\left| \mathbf{\nabla} \times \left( \frac{-k}{r^{2}} \right) \mathbf{\hat{e}}_{r} \right|\right| &=& \frac{d}{dx} \left[ \frac{1}{2} \left(x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \cdots \right) \left( \frac{x}{\sin x} - \cos x \right) \right] - \int_{0}^{\frac{\pi}{2}} \cos x \ dx \\
0 &=& 1 - 1 \\
&=& 0 
\end{eqnarray*}

\end{document}

[Durandal]

someone should code something into phpBB that allows you to display mathematical notation. I'm sure I could figure out some way, but then, I am not the person at phpBB.

There's MathML, but as Phong said, support for it in browsers is pretty slim at the moment, relegating those in the scientific community to resort to really shitty-looking GIF's to display equations. I'm sure that, if it ever becomes widely accepted, the phpBB people could add in an option for board admins to enable or disable MathML (but not necessarily HTML) on their boards.

But for now, we're stuck with my little PNG method for doing things.