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I thought that a circular disc in $\mathbb{R^2}$ is a convex set with the extreme points being that of the perimeter, and the right circular cone in $\mathbb{R^3}$ is similar in that it is the convex set with the extreme points being its vertex and the base circle. My teacher agreed with my solution but then changed his mind.

Is there a mistake in my solution?

Jam
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  • According to the definition https://en.wikipedia.org/wiki/Extreme_point IMO only the vertex and the points of the base circumference are extremes, not the internal points of the base circle – Raffaele Dec 24 '20 at 21:08
  • yes that is why i said circle instead of a disc because circle is a curve not an region (i am not english native so i am not sure if it is normal in english to refer to the area enclosed by a circle using just the word circle so i said circular disc ) – Jam Dec 24 '20 at 22:45

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