diagonal argument

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    Hidden assumption of the diagonal argument

    This article uncovers a hidden assumption that the diagonal argument needs, then, explains its implications in matter of infinity. The use of the diagonal digits imposes a condition unnoticed until now. If this assumption were found false, the conclusion of the diagonal argument should be...
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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...