| 1. | The Cartesian product of an infinite set and a nonempty set is infinite.
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| 2. | Now let X be a nonempty set.
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| 3. | Let be a nonempty set and let denote the set of all finite subsets of.
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| 4. | Let M be a nonempty set.
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| 5. | Then, every number maps to a nonempty set and no number maps to the empty set.
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| 6. | Let X be an arbitrary nonempty set and let G be a commutative semigroup acting on X.
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| 7. | Let \ mathbb { T } be a nonempty collection of nonempty sets of attribute-value pairs.
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| 8. | These entities form the domain of discourse or universe, which is usually required to be a nonempty set.
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| 9. | The union of a nonempty set of ordinals that has no greatest element is then always a limit ordinal.
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| 10. | If sets are admitted, M8 asserts the existence of the fusion of all members of any nonempty set.
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