| 21. | Every regular ordinal is the initial ordinal of a cardinal.
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| 22. | No ordinal rankings are used to determine the final results.
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| 23. | The most common scale of measurement is the ordinal Mohs hardness scale.
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| 24. | Then transfinite induction tells us that P is true for all ordinals.
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| 25. | All three cases are identical except for the type of ordinal considered.
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| 26. | Ordinal utility functions are unique up to increasing monotone transformations.
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| 27. | Every countable limit ordinal requires replacement for its construction analogously to ??.
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| 28. | In the 14th century, Emperor Charles IV sometimes used that ordinal.
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| 29. | This violates the axiom of transitivity for the ordinal scale.
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| 30. | There are practical reasons : consorts do not have ordinals.
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