| 1. | Here " E " may be a finite or an infinite set.
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| 2. | A finite set has a smaller cardinality than an infinite set, right?
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| 3. | He called the cardinal numbers of these infinite sets transfinite cardinal numbers.
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| 4. | The other is that we may quantify over infinite sets without restriction.
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| 5. | Any set which can be mapped onto an infinite set is infinite.
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| 6. | In the nineteenth century some infinite sets are strictly larger than others.
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| 7. | "' Combinatorial set theory "'concerns extensions of finite combinatorics to infinite sets.
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| 8. | Infinite sets larger than this are said to be " uncountable ".
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| 9. | There are lots of perfectly good probability distributions on a countably infinite set.
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| 10. | In the case of infinite sets, the behavior is more complex.
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