Is this statement for proving inequalities true?

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    Inequalities
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Discussion Overview

The discussion revolves around the validity of a proposed method for proving inequalities, specifically whether knowing that ##a > c## and proving ##c < b## can imply ##a < b##. Participants explore the implications of these inequalities and whether the proposed reasoning is a recognized theorem.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant proposes that if ##a < b## and ##a > c##, proving ##c < b## could imply ##a < b##.
  • Another participant challenges this reasoning, asking for a counterexample to demonstrate its potential flaw.
  • A later reply acknowledges a misunderstanding in the initial reasoning, suggesting that the logic presented was incorrect.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there is disagreement regarding the validity of the proposed implication and the reasoning behind it.

Contextual Notes

The discussion highlights a potential misunderstanding in the application of inequalities, but does not resolve the underlying mathematical principles or assumptions involved.

Physicist97
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Hello! What I'm wondering is if you want to prove an inequality, let's say ##a<b## and you already know that ##a>c## is true. If you are able to prove that ##c<b## is true, would that go on to imply that ##a<b## is true also? If this is correct, is it known as a theorem?

Thank you!
 
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No. Can you find a counterexample?
 
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Physicist97 said:
Hello! What I'm wondering is if you want to prove an inequality, let's say ##a<b## and you already know that ##a>c## is true. If you are able to prove that ##c<b## is true, would that go on to imply that ##a<b## is true also? If this is correct, is it known as a theorem?

Thank you!

In other words:

##c < a## and ##c < b## implies ##a < b##

There's something not right there.
 
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Mhmm, yea I see where I went wrong haha. It was a pretty silly mistake, too :). Thank you everyone.
 

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