Abstract In 1914, Felix Hausdorff published an elegant proof that almost all numbers are simply normal in base 2. We generalize this to show normal. The result is arguably the most elementary for theorem so far and should be accessible undergraduates their first year.

A bstract We investigate the geometry near horizon of a generic, four-dimensional extremal black hole. When cosmological constant is negative, we show that (in almost all cases) tidal forces diverge as one crosses horizon, and this singularity stronger for larger holes. In particular, applies to generic nonspherical holes, such those satisfying inhomogeneous boundary conditions. Nevertheless, s...