Cardinal number: irrationals vs fractals

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SUMMARY

The cardinal number for the set of irrational numbers is equivalent to that of the real numbers, denoted as c. Fractals, being continuous subsets of the plane, also possess a cardinality of c. Therefore, both the set of irrational numbers and any continuous subset, including fractals, share the same cardinality, which is c.

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  • Understanding of cardinal numbers in set theory
  • Familiarity with real numbers and their properties
  • Basic knowledge of fractals and their mathematical definitions
  • Concept of continuous subsets in topology
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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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