A set $C$ is *convex* if for all
$x,y \in C$ and for all
$\alpha \in [0,1]$ the point
$\alpha x + (1-\alpha) y \in C$.

There are no natural numbers
$\naturals = (1, 2, 3, \ldots)$
$x$, $y$, and $z$ such that
$x^n + y^n = z^n$, in which $n$
is a natural number greater than 2.