TITLE: Cardinality of the Mandelbrot set
QUESTION [8 upvotes]: Is the Mandelbrot set countable or of the cardinality $2^{\aleph_0}$? My intuition says the latter, but I couldn't find a bijection.

REPLY [18 votes]: $M$ is a subset of $\Bbb R^2$ and contains the open disk of radius $\frac14$ around the origin, i.e., $M$ is "between" two sets of cardinality $2^{\aleph_0}$, hence itself of cardinality $2^{\aleph_0}$.