Is the interior of an angle a convex set?

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Discussion Overview

The discussion revolves around proving that the interior of angle

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • Some participants assert that the interior of
  • There is a suggestion that proving the intersection of two convex sets is also convex would be a critical step in the argument.
  • One participant seeks guidance on how to prove that the intersection of two half planes is convex.
  • Another participant begins outlining a proof by considering points p and q in the intersection of two convex sets, indicating a potential approach to the proof.

Areas of Agreement / Disagreement

Participants generally agree on the premise that the interior of

Contextual Notes

Limitations include the need for a clear demonstration of the convexity of the intersection of half planes and the assumptions regarding the properties of convex sets that are not fully articulated.

LCharette
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I need to prove the interior of <ABC is a convex set. I know it is. I started by defining the angle as the intersection of two half planes and using the fact that each half plane is convex. I am stuck on where to go from here.
 
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LCharette said:
I need to prove the interior of <ABC is a convex set. I know it is. I started by defining the angle as the intersection of two half planes and using the fact that each half plane is convex. I am stuck on where to go from here.

If you could prove the intersection of two convex sets is convex as well you'd be set
 
Do you have any suggestions on how to prove the intersection of two half planes is convex?
 
Let p and q be in the intersection of convex sets A and B.

p and q are both in A so ...

p and q are both in B so ...
 

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