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    For every ordinal number there is a corresponding aleph c... — Carmelics
    Home/Modality & Possibility
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    Supports→There is an infinite hierarchy of infinite cardinal numbers

    For every ordinal number there is a corresponding aleph cardinal

    Modality & Possibility
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    Ordinal numbers designate each cardinal's position in their well-orderingThere is an infinite hierarchy of infinite cardinal numbersThere is an infinite hierarchy of infinite ordinal numbers

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    Every cardinal number can be represented by an ordinal number81%There is no set of all cardinal numbers and no set of all ordinal numb...76%If there were an ordinal corresponding to the order type of the set of...74%There is an infinite hierarchy of infinite ordinal numbers73%

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    Thus, just as there is an infinite hierarchy of infinite ordinal numbers, which Cantor represented with lowercase Greek letters, there is also an infinite hierarchy of infinite cardinal numbers, which Cantor represented with Hebrew letters, and in particular aleph, “\(\aleph\)”. The finite cardinals are 0, 1, 2, 3, …. The first infinite cardinal, that of the natural numbers (and all countable sets), is \(\aleph_0\). Cantor’s “well-ordering principle”, stating that every set can be put into some

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