Theorems about convex functions often look like the following:(adsbygoogle = window.adsbygoogle || []).push({});

Let f: S->R where S is a convex set.

Suppose f is a convex function.......

So here are my questions:

1) For a convex function, why do we always need the domain to be convex set in the first place?

2) Can a convex function be discontinuous?

Thanks for any inputs.

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# Convex set and convex functions

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