continuum hypothesis

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    Continuous set and continuum hypothesis

    This article explains why the cardinality of a set must be either Aleph0 or |ℝ|. 1. Rational numbers are discrete 2. Real numbers are continuous 3. Collectively exhaustive and mutually exclusive events 4. Continuum hypothesis 5. Cardinality of discontinuous subsets of real numbers...
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    Cardinality of the set of binary-expressed real numbers

    This article gives the cardinal number of the set of all binary numbers by counting its elements, analyses the consequences of the found value and discusses Cantor's diagonal argument, power set and the continuum hypothesis. 1. Counting the fractional binary numbers 2. Fractional binary...