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The Proof is Trivial!

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Original post by und
It's very similar to a STEP question I've seen, but I can't remember which paper. DJ will know obviously. :tongue: I think it could have been posed as a general question, because numbers are yucky. :yucky:


That's quite a good idea and would probably make the question more STEP style.
Original post by und
It's very similar to a STEP question I've seen, but I can't remember which paper. DJ will know obviously. :tongue: I think it could have been posed as a general question, because numbers are yucky. :yucky:


I do actually know which one you mean (I think they use a chicken crossing a road in the specific question as well) but I can't for the life of me remember which paper it was from.
Reply 262
Original post by DJMayes
I do actually know which one you mean (I think they use a chicken crossing a road in the specific question as well) but I can't for the life of me remember which paper it was from.

That's the one. I believe it was a STEP I Q9, but I don't know which paper.
Original post by und
That's the one. I believe it was a STEP I Q9, but I don't know which paper.


1997 STEP I Q9. Will have to go back and do that tomorrow as I skipped over it when I first saw it (Which was back in November, but still).
Original post by Felix Felicis
Do I really have that many holes in my solutions? :s-smilie: Would you mind pointing one or two out? :colondollar:



No of course not. I was joking, with slight innuendo :biggrin:
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Original post by bananarama2
Well all of particle physics is to do with symmetry groups, which slightly related to sets (isn't it?), so....there is potential.

Heck. The Higgs mechanism is to do with symmetry breaking.


Groups to Sets is like Chemistry to Physics.
Problem 47 *** (came across this nice problem thanks to a friend :biggrin:)

For 0<p<q0 < p< q, evaluate

xsinx(x2+p2)(x2+q2) dx\displaystyle \int_{-\infty}^{\infty} \dfrac{x \sin x}{(x^2 + p^2)(x^2 +q^2)} \ dx

and deduce that

xcosx(x2+p2)(x2+q2) dx=0\displaystyle \int_{-\infty}^{\infty} \dfrac{x \cos x}{(x^2 + p^2)(x^2 +q^2)} \ dx = 0
(edited 10 years ago)
Reply 267
Original post by ukdragon37
That's exactly what I've been thinking, but I can't come up with anything either.


shamika
blah


http://en.wikipedia.org/wiki/Causal_sets

might be of interest
Original post by ukdragon37
That's exactly what I've been thinking, but I can't come up with anything either.


have you done topos theory?
http://math.ucr.edu/home/baez/topos.html
has some nice links to physics
Original post by ben-smith
have you done topos theory?
http://math.ucr.edu/home/baez/topos.html
has some nice links to physics


A little, yes. But then topos theory is quite a different beast to set theory. :tongue:
I just wanne say Math is sexy !!

( more i dont know because i am a musician/and former model )
Original post by Noble.
...


Spoiler

Solution 47

xsinx(x2+p2)(x2+q2)dx=1q2p2(xsinxx2+p2dxxsinxx2+q2dx)\displaystyle\int_{-\infty}^{\infty} \frac{x\sin x}{(x^2+p^2)(x^2+q^2)}\,dx=\frac{1}{q^2-p^2}\left(\int_{-\infty}^{\infty} \frac{x\sin x}{x^2+p^2}\,dx-\int_{-\infty}^{\infty} \frac{x\sin x}{x^2+q^2}\,dx\right)

f(t)=0sintxdxx2+λ2dxL{f(t)}=0est0xsintxdxx2+λ2dxdt=0xx2+λ20estsintxdtdx=0x2(x2+λ2)(x2+s2)dx=π2(s+λ)\displaystyle \begin{aligned}f(t)=\int_0^{ \infty} \frac{\sin tx\,dx}{x^2+\lambda^2}\,dx \Rightarrow \mathcal{L} \{ f(t)\} &=\int_0^{ \infty}e^{-st}\int_0^{ \infty}\frac{x\sin tx\,dx}{x^2+ \lambda^2}\,dx\,dt\\&=\int_0^{ \infty}\frac{x}{x^2+ \lambda^2}\int_0^{\infty}e^{-st}\sin tx\,dt\,dx\\&=\int_0^{\infty} \frac{x^2}{(x^2+ \lambda^2)(x^2+s^2)} \,dx\\&= \frac{\pi}{2(s+\lambda)}\end{aligned}

L1{πs+λ}=πeλ(=xsinxx2+λ2dx)\displaystyle \mathcal{L}^{-1}\left\{ \frac{\pi}{s+\lambda}\right\}= \frac{\pi}{e^{\lambda}}\quad \left( = \int_{-\infty}^{\infty} \frac{x\sin x}{x^2+\lambda^2}\,dx\right)

Hence
Unparseable latex formula:

\displaystyle\int_{-\infty}^{\infty} \frac{x\sin x}{(x^2+p^2)(x^2+q^2)}\,dx = \frac{\pi}{q^2-p^2}\left(\frac{1}{e^p}-\frac{1}{e^q}\right)\end{aligned}

(edited 10 years ago)
Reply 273
Original post by Lord of the Flies
k=l=m=1,  p=n=3k = l = m = 1,\; p = n = 3 satisfies that equation. Is there something missing from the question?


Original post by metaltron
What's even more worrying is p isn't congruent to -1mod8. I just spent ages on this question!


Gentlemen, I beg your pardon. The condition should be p>3p > 3.
(edited 10 years ago)
Original post by Star-girl

Spoiler



I ended up with zero as well, all though I didn't have to substitute anything. I thought I'd got it wrong and I couldn't see why, so I gave up.
Original post by ukdragon37
Groups to Sets is like Chemistry to Physics.


So one uses the other a little bit?
Original post by bananarama2
I ended up with zero as well, all though I didn't have to substitute anything. I thought I'd got it wrong and I couldn't see why, so I gave up.


Maybe it is so... but then how to link the next part with the previous part...
Guys, Indeterminate's integral should actually be problem 47.
Original post by bananarama2
So one uses the other a little bit?


Somewhat, yes.

If set theory is Physics, then
group theory is Chemistry,
field theory is Biology,
and category theory is Philosophy.

:tongue:
(edited 10 years ago)
Original post by ukdragon37
Somewhat, yes.

If set theory is Physics, then
group theory is Chemistry,
field theory is Biology,
and category theory is Philosophy.

:tongue:


(quantum) Field theory looks so interesting!

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