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The Proof is Trivial!

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Original post by CherGalois
you used my hint well young padawan...maybe you should aim to apply to warwick :biggrin:


I did not use any hints of yours, and I am already at university...
Original post by DJMayes
I did not use any hints of yours, and I am already at university...


No need to get so defensive, a good mathematician knows when to ask for help :smile:
Original post by CherGalois
No need to get so defensive, a good mathematician knows when to ask for help :smile:


I don't know what you're taking but I want some.
Original post by Khallil
I too, would like a hit of what you're taking :wink:


Original post by DJMayes
I don't know what you're taking but I want some.


i understand that my mathematical ability may well look so astonishing to you that it requires an unnatural means to be as good as me, but i can assure you this is not so. Atleast i waited till morning to reply so you could have one last dream, one last hope...

unfortunately, my mathematical abilities are intrinsically natural and have only been developed thus far due to my own natural abilities.

This is the same for all oxford mathmos....maybe one day with all your hard work you may bathe in a glory similar to mine.
Original post by CherGalois
i understand that my mathematical ability may well look so astonishing to you that it requires an unnatural means to be as good as me, but i can assure you this is not so. Atleast i waited till morning to reply so you could have one last dream, one last hope...


What a truly thoughtful sentiment. You are indeed a wonderful person.

Original post by CherGalois
unfortunately, my mathematical abilities are intrinsically natural and have only been developed thus far due to my own natural abilities.



Original post by CherGalois
This is the same for all oxford mathmos....maybe one day with all your hard work you may bathe in a glory similar to mine.


One day :moon:
(edited 10 years ago)
Original post by Khallil
What a truly thoughtful sentiment. You are indeed a wonderful person.






One day :moon:


Aren't all mathematicians :wink:
Reply 2546
Avatar for Flauta
Flauta
9
Original post by CherGalois
Aren't all mathematicians :wink:

I can think of a few who aren't.

Problem 419***

Evaluate ∫−∞∞cos⁡(x)x4+1 dx\displaystyle\int_{-\infty}^{\infty}\dfrac{\cos(x)}{x^4+1}\ dx
(edited 10 years ago)
Original post by Flauta
I can think of a few who aren't.

Problem 419***

Evaluate ∫−∞∞cos⁡(x)x4+1 dx\displaystyle\int_{-\infty}^{\infty}\dfrac{\cos(x)}{x^4+1}\ dx


such as?
Reply 2548
Avatar for Flauta
Flauta
9
Original post by CherGalois
such as?

That would be very mean, I don't tolerate bullying.

Prove an answer to my problem :^_^:
Original post by Flauta
That would be very mean, I don't tolerate bullying.

Prove an answer to my problem :^_^:


just as in maths where proving something exists is fundamentally more important than finding what actually exists, pointing out that such mathematicians exist is just as much bullying as is naming them

i think id rather evaluate it and derive an answer, than prove an answer as i have not yet attained an answer to prove,but when i do the process of proving it would be futile as my method of evaluation satisfies this proof you so desire
Reply 2550
Avatar for Flauta
Flauta
9
Original post by CherGalois
just as in maths where proving something exists is fundamentally more important than finding what actually exists, pointing out that such mathematicians exist is just as much bullying as is naming them

i think id rather evaluate it and derive an answer, than prove an answer as i have not yet attained an answer to prove,but when i do the process of proving it would be futile as my method of evaluation satisfies this proof you so desire


What I meant was to post your working rather than just an answer :tongue: No need to be so pernickety lol
Original post by Flauta
What I meant was to post your working rather than just an answer :tongue: No need to be so pernickety lol


as you may have noticed i revel in being extreme and having a bit of fun on here
Reply 2552
Avatar for 1298977
1298977
1
Umm, hey, does anyone have some nice problems on combinatorics? Or on elementary number theory? I feel like solving problems, but not scary integrals. :s-smilie:
Original post by CherGalois
Aren't all mathematicians :wink:


I was using sarcasm.
Original post by Khallil
I was using sarcasm.


and i was ignoring it so that you thought i didnt realise your sarcasm and made you think that i had taken it as a compliment. this then annoyed you as you might be fairly petty (but then isnt everyone) and you were so frustrated inside that you couldnt let me think that you had complimented me, such approval which i really dot require anyway, that you not only identified it as sarcasm after, but posted a link to wiki as you were so threatened by my mathematical superiority that you had to appear superior in an altogether insignificant, yet different way

g'day sir :hat2:
Original post by CherGalois
and i was ignoring it so that you thought i didnt realise your sarcasm and made you think that i had taken it as a compliment. this then annoyed you as you might be fairly petty (but then isnt everyone) and you were so frustrated inside that you couldnt let me think that you had complimented me, such approval which i really dot require anyway, that you not only identified it as sarcasm after, but posted a link to wiki as you were so threatened by my mathematical superiority that you had to appear superior in an altogether insignificant, yet different way

g'day sir :hat2:


Spoiler


If you'd like to discuss this further, I'm more than happy to continue our discussion via PM so as not to derail this thread any further. (Which is why I put my response in a spoiler)
(edited 10 years ago)
Original post by Flauta
I can think of a few who aren't.

Problem 419***

Evaluate ∫−∞∞cos⁡(x)x4+1 dx\displaystyle\int_{-\infty}^{\infty}\dfrac{\cos(x)}{x^4+1}\ dx


Can we use contour integrals, or is that cheating?
Original post by Flauta
Problem 419***

Evaluate ∫−∞∞cos⁡(x)x4+1 dx\displaystyle\int_{-\infty}^{\infty}\dfrac{\cos(x)}{x^4+1}\ dx


This is merely an exercise if one knows a bit of complex analysis, and is a massive slog otherwise...

Here is something for the new year!

Problem 420**

If ∑k≥0xk\displaystyle \sum_{k\geq 0}x_k converges, does ∑k≥0xk2014\displaystyle \sum_{k\geq 0}x_k^{2014} converge?? What about ∑k≥0xk2013?\displaystyle \sum_{k\geq 0}x_k^{2013}?

Problem 421***

∫−∞∞[1+(1x+1+2x+2+⋯+2013x+2013−x)2014]−1 dx\displaystyle \int_{-\infty}^{\infty} \left[1+\left(\frac{1}{x+1}+\frac{2}{x+2}+\cdots +\frac{2013}{x+2013}-x\right)^{2014}\right]^{-1}\,dx
Original post by Lord of the Flies

Problem 420**

If ∑k≥0xk\displaystyle \sum_{k\geq 0}x_k converges, does ∑k≥0xk2014\displaystyle \sum_{k\geq 0}x_k^{2014} converge?? What about ∑k≥0xk2013?\displaystyle \sum_{k\geq 0}x_k^{2013}?


Solution 420

First is a no, consider (−1)nn12014\frac{(-1)^n}{n^{\frac{1}{2014}}}, this converges by the alternating series test, but 1/n is well known to diverge.

Second is a yes, but this proof of this requires some fiddling with episilon and deltas in the definition of convergance and is not particularly interesting. The best way to look at it qualitively is that it preserves signs, and the xkx_k terms tend to 0, and the power of 2013 only makes them do this faster so it converges. I know this is not a proof, but the proof goes along these lines, just with more rigour.
Original post by james22
Second is a yes, but this proof of this requires some fiddling with epsilon and deltas in the definition of convergence and is not particularly interesting.


If you try proving it, you will find that it is more interesting than it initially looks. :biggrin:

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