Cardinal number: irrationals vs fractals

[Loren Booda]

How does the cardinal number for the set of irrational numbers compare to that for a fractal set?

[mathman]

Cardinal number for irrationals is the same as for reals, i.e. c. Fractals (if I understand what you are driving at) form a continuous subset of the plane. Since the cardinality of points in the plane is also c, any continuous subset will have cardinality c.