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    The well-ordering principle is equivalent to the Axiom of... — Carmelics
    Home/Modality & Possibility
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    Supports→Every cardinal number can be represented by an ordinal number

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

    Modality & Possibility
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    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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    Cantor's well-ordering principle states that every set can be put into...89%The restricted principle that all well-founded sets are well-orderable...78%Apriori ordering principles can never conflict with experience and are...77%Ordinal numbers are defined as equivalence classes of well-orderings u...77%

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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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