Going Senile at 30: Question on Stack Exchange

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Discussion Overview

The discussion revolves around a question posted on Stack Exchange regarding the limit of an integral involving the function \( e^{iz} \) as the contour approaches infinity. Participants express their thoughts on the complexity of the problem, feelings of inadequacy, and humorous reflections on age and mental sharpness.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions whether \( \lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0 \) is trivial, expressing feelings of potential senility.
  • Another participant acknowledges the difficulty in seeing the limit at first glance and mentions the challenge of finding an upper bound.
  • A participant reflects on the elementary antiderivative of \( e^{iz} \) and notes the lack of justification for bringing the limit inside the integral.
  • Some participants agree that recognizing the behavior of functions along contours in complex analysis can be challenging.
  • Humorous remarks about age and mental sharpness are shared, with participants joking about feeling "senile" at various ages.
  • One participant suggests that sometimes taking it easy can help in finding solutions to problems.
  • A later post humorously inquires about the converse of Morera's theorem, indicating a light-hearted tone in the discussion.

Areas of Agreement / Disagreement

Participants express a range of feelings about their mental acuity and the complexity of the problem, but there is no consensus on the original question regarding the limit of the integral. Multiple competing views and humorous reflections remain present throughout the discussion.

Contextual Notes

Participants mention the difficulty in applying complex analysis techniques and the nuances involved in justifying steps in the evaluation of the integral. There is an acknowledgment of the challenges posed by the problem without resolving them.

Who May Find This Useful

This discussion may be of interest to individuals exploring complex analysis, particularly those grappling with limits and integrals, as well as those who enjoy light-hearted exchanges about age and mental sharpness in mathematical contexts.

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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.
 
Last edited:
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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