Cardinal number: irrationals vs fractals

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

mathman

Science Advisor
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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.
 

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