Prove that A:B is greater than C:D?

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    Mathematics Theory
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Discussion Overview

The discussion revolves around proving the inequality of ratios A:B and C:D based on certain mathematical conditions. It involves exploring the relationships between these ratios and their components, with a focus on mathematical reasoning.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant references "Road to Reality" and states that A:B is greater than C:D if certain conditions involving the sums of A, B, C, and D are met.
  • Another participant proposes that if A(M+1) > B(N+1) and D(N+1) > C(M+1), then it follows that A/B > (N+1)/(M+1) and C/D < (N+1)/(M+1), suggesting this proves A:B > C:D.
  • A later reply emphasizes that the conclusions drawn are based on the assumption that all numbers involved are positive.
  • There are also comments regarding the appropriate forum for the discussion, indicating some uncertainty about the categorization of the thread.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate forum for the discussion, but there is no consensus on the mathematical proof itself, as the reasoning is presented with conditions and assumptions.

Contextual Notes

The discussion assumes positivity of the involved numbers, which may limit the applicability of the conclusions drawn. Additionally, there are unresolved aspects regarding the categorization of the thread.

Julia Coggins
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From "Road to Reality" chapter 3 part two. If three ratios are known: M:N, A:B, C:D. A:B is greater than C:D if: A added to itself M times exceeds B added to itself N times and D added to itself N times exceeds C added to itself M times. Show that the ratio A:B is greater than C:D.
 
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I believe this should be posted in maths forum.
Based on the data,
A(M+1)>B(N+1) and D(N+1)>C(M+1)
So,
A/B>(N+1)/(M+1)...(1)
and
C/D<(N+1)/(M+1)...(2)
1 and 2 clearly prove A:B>C:D.
 
Thank you, it does belong to the mathematics category, but I'm unsure how to change it
 
Julia Coggins said:
but I'm unsure how to change it
You can't change it once you've posted it. A mentor will fix it.
 
Ah I see. Once again, thank you, I suppose for some reason I struggled with an otherwise simple question.
 
cnh1995 said:
I believe this should be posted in maths forum.
Based on the data,
A(M+1)>B(N+1) and D(N+1)>C(M+1)
So,
A/B>(N+1)/(M+1)...(1)
and
C/D<(N+1)/(M+1)...(2)
1 and 2 clearly prove A:B>C:D.
This is assuming all the numbers involved are positive.
 
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