Is There a Difference Between These Two Notations for Infinite Summation?

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Discussion Overview

The discussion revolves around the notational differences between \(\lim_{n\rightarrow\infty}\sum_{i=1}^{n}\) and \(\sum_{n=1}^{\infty}\) in the context of infinite summation. Participants explore whether these notations convey different meanings or if they are essentially equivalent.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions if there is a difference between the two notations for infinite summation.
  • Another participant suggests that the latter notation is defined as the former, implying equivalence.
  • A third participant humorously notes that the difference may be trivial, relating it to the amount of ink or LaTeX code used.
  • A fourth participant adds a lighthearted comment about the financial constraints of math departments, further emphasizing the triviality of the difference.

Areas of Agreement / Disagreement

Participants appear to agree that the difference is minimal, focusing on the notational aspect rather than any substantive mathematical distinction. However, the initial question about the difference indicates some level of uncertainty or debate.

Contextual Notes

The discussion does not delve into deeper mathematical implications or definitions that may clarify the notational differences further.

Icebreaker
Is there a difference between [tex]\lim_{n\rightarrow\infty}\sum_{i=1}^{n}[/tex] and [tex]\sum_{n=1}^{\infty}[/tex]?
 
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Nevermind. The latter is defined as the former.
 
Yes,that means that the difference is only in writing...One required less ink (or LaTex code) than the other...:-p

Daniel.
 
Ya, the math departments are so strapped for cash they must conserve ink. :smile:
 

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