Can someone teach me Brouwer's fixed point theorem? I am feeling inadequate.
in the simplest of terms, a fixed point theorem means that a function
f has one or more points for which
f(x) = x.
Brouwer's fixed point theorem states that for any continuous function
f, mapping a compact convex set to itself, there is a point
x_0 where
f(x_0) = x_0 holds. Compactness means we're dealing with a subset of euclidian space which is bounded and closed. A convex set basically means we have a shape in which you can choose two arbitrary points and connect them. Every point that's on the line segment between these two points is in the shape, otherwise it's not a convex set.
Hope that clears things up.
Do i get to brag about my IQ now pls?