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    The definition of ordinal numbers ensures that for any no... — Carmelics
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    Supports→Every cardinal number can be represented by an ordinal number

    The definition of ordinal numbers ensures that for any non-empty set of ordinal numbers there is always a first element

    Modality & Possibility
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    Every cardinal number can be represented by an ordinal number

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    Cantor's well-ordering principle states that every set can be put into some well...Every cardinal number can be represented by an ordinal number

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    The well-ordering principle is equivalent to the Axiom of Choice

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    For any non-empty set of ordinal numbers there is always a first ordin...93%The natural order on ordinal numbers is a set in NFU81%There is no set of all cardinal numbers and no set of all ordinal numb...80%The operation T on ordinal numbers can be defined in NFU80%

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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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