Cardinal number: irrationals vs fractals

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The cardinal number for the set of irrational numbers is the same as that for the real numbers, denoted as c. Fractals are considered continuous subsets of the plane. Since the cardinality of points in the plane is also c, any continuous subset, including fractals, will also have a cardinality of c. This means both irrational numbers and fractal sets share the same cardinality. Understanding these relationships highlights the similarities in the size of these mathematical sets.
Loren Booda
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How does the cardinal number for the set of irrational numbers compare to that for a fractal set?
 
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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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