$ \text{If } S = \{\alpha \in R^3 | \alpha_1 + \alpha_2 e^{-t} + \alpha_3 e^{-2t} \leq 1.1 \text{ for } t \geq 1\}$, then

1) S is affine

2) S is convex

3) S is a polyhedron


1) Is an affine set the same thing as an affine hull?

I've only had a handwavy background in convexity so I think of something being affine as it being a straight line translated on some axis so I don't think that this is true?

2 & 3) I have no intuition regarding convexity and polyhedron. I'm thinking of choosing some arbitrary $\alpha_a \text{ and } \alpha_b$ and going through the definition. Is there a better way to do this?


Partial answer:

An affine hull is a particular affine set (smallest affine set containing the given set).

An affine set can be thought of as a translation of a vector space; your example is correct, but it could also be a translated plane etc.


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