MHB Going Senile at 30: Question on Stack Exchange

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The discussion revolves around a question posted on Stack Exchange regarding the limit of an integral involving the function e^{iz} as R approaches infinity. Participants express their initial confusion about the problem, with some humorously questioning their own mental sharpness at a young age. The conversation highlights the challenges of applying complex analysis, particularly the difficulty in justifying the interchange of limits and integrals. Acknowledgment of the function's elementary antiderivative is mentioned, but participants reflect on how trivial aspects can be overlooked when dealing with complex problems. The tone remains light-hearted, with jokes about age and mental acuity, emphasizing the importance of taking a step back to simplify complex issues.
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Random Variable said:
Yesterday I posted a question on Stack Exchange that was so trivial that I think I might be going senile at the age of 30. That, or I was under the influence of something.

Does $\lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0$? (Drunk)

Yeah, I must confess , that wasn't easy to see at the first glance, at least for me. I was trying just like you to find an upper bound (Headbang)
 
Well, I guess I am going senile at the age of 23 (Worried)
 
And then mrf had to rub it in by mentioning that $e^{iz}$ of course has an elementary antiderivative that is valid everywhere since $e^{iz}$ is an entire function.

I could have at least recognized that there was no justification for bringing the limit inside of the integral due to the fact that parametrization of the integral brings an $R$ out front.
 
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Actually, it isn't always easy to see that a function along a contour approaches zero for large or small quantities of the modulus. It is always the hard part when using complex analysis approaches.

I recognized that the function has an anti-derivative but that was a little bit late .
 
I went senile already. Wasn't working for me.
 
Random Variable said:
Yesterday I posted a question on Stack Exchange that was so trivial that I think I might be going senile at the age of 30. That, or I was under the influence of something.

Does $\lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0$? (Drunk)

If You allow an 'oversixty' to do You a suggestion, then the suggestion is...

... sometime just take it easy! (Happy)...

Kind regards

$\chi$ $\sigma$
 
I am already senile at 13. I once thought about a long time why there is no prime $\geq 3$ of the form $x^3+y^3$. :p
 
mathbalarka said:
I am already senile at 13...

Yes you are, since you are now 14. :D
 
  • #10
Ah, but I will refer myself as 13 ever afterwards until 17, as 14 is not of my likes, neither is 15 or 16!
 
  • #11
mathbalarka said:
Ah, but I will refer myself as 13 ever afterwards until 17, as 14 is not of my likes, neither is 15 or 16!

I guess if Jack Benny could be 39 forever, then you can be 13 for a few years. :D
 
  • #12
I'm in my mid twenties and often feel I'm just not as sharp as I used to be. Doesn't bode well for my 30's and 40's. :p
 
  • #13
chisigma said:
If You allow an 'oversixty' to do You a suggestion, then the suggestion is...

... sometime just take it easy! (Happy)...

Kind regards

$\chi$ $\sigma$

True. Working with some complicated stuff , you always miss the trivial. Sometimes it needs no more than thinking simple to find the solution.
 
  • #14
Random Variable said:
Yesterday I posted a question on Stack Exchange that was so trivial that I think I might be going senile at the age of 30. That, or I was under the influence of something.

Does $\lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0$? (Drunk)
That's why I drink so much- so I can claim I'm not senile.:p
 
  • #15
Is there a converse of Morera's theorem? (Smirk) :p
 
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