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    For any non-empty set of ordinal numbers there is always ... — Carmelics
    Home/Modality & Possibility
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    Supports→The cardinal numbers must be well-ordered

    For any non-empty set of ordinal numbers there is always a first ordinal number

    Modality & Possibility
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    Modality & Possibility

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    Every cardinal number can be represented by an ordinal numberThe cardinal numbers must be well-ordered

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    The definition of ordinal numbers ensures that for any non-empty set o...93%

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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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