Why correct this inequality log(d/d-1)>(1/d)?

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Discussion Overview

The discussion revolves around the inequality log(d/(d-1)) > 1/d for d ≥ 2. Participants explore the validity of this inequality and suggest methods for proving or analyzing it, including checking specific values and examining derivatives.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the formulation of the inequality, suggesting there may be a mistake since d/d = 1.
  • Another participant expresses confusion over the expression d/d - 1, interpreting it as a potential misrepresentation of the inequality.
  • A suggestion is made to verify the inequality for d = 2 and to analyze the behavior of the function log(d/(d-1)) compared to 1/d for values greater than 2.
  • Participants propose using the derivative of the function or plotting the functions to gain insight into the inequality's validity.
  • There is a recommendation to study the function log(d/(d-1)) - 1/d to analyze its behavior and values for specific d.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the inequality, and multiple viewpoints regarding its formulation and analysis remain present.

Contextual Notes

Some assumptions about the behavior of the functions and the conditions under which the inequality holds are not fully explored, leaving room for further analysis.

parisa
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Why correct this inequality,

log(d/(d-1))>1/d for d≥2?
 
Last edited:
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There must be a mistake in your question since d/d=1
You corrected the mistake.
 
Last edited:
multiplication comes before addition.
I see d/d-1 as [tex]\frac{d}{d} -1[/tex]log 0 = who-knows-what
 
Well, check first that this inequality is correct for d=2.
Then prove that the function log(d/(d-1)) will continue to be > than 1/d for d>2.
You could do that by analysis the derivative.

Get insight by making a plot of these functions.

Alternatively, study the function log(d/(d-1))-1/d .
Calculate its value for d=2, and analyze its behavior for d>2 .
 
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