The Set of Convex Functions is Convex

We show that the set of convex functions f : V → ℝ is a convex set, for each fixed V, where V is a real vector space (or a convex subset of a real vector space). Some animations are included to help visualise linear combinations of convex functions.

00:00 Intro
00:14 Definition - convex set
01:31 Definition - convex function
03:36 Animation example 1
05:03 Animation example 2
05:38 Bonus fun fact!
06:30 Proof - the set of convex functions is convex