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Cake day: July 2nd, 2023

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  • no, there aren’t enough integers to map onto the interval (0,1).

    probably the most famous proof for this is Cantor’s diagonalisation argument. though as it usually shows how the cardinality of the naturals is small than this interval, you’ll also need to prove that the cardinality of the integers is the same as that of the naturals too (which is usually seen when you go about constructing the set of integers to begin with)