| 1. | Thus absolute continuity induces a partial ordering of such equivalence classes.
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| 2. | Real numbers are defined as the equivalence classes of this relation.
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| 3. | The equivalence classes of this relation are called germs at infinity.
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| 4. | One of the most common uses equivalence classes of geodesic rays.
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| 5. | The real projective line is the set of all equivalence classes.
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| 6. | This circle intersects each equivalence classes in exactly two opposite points.
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| 7. | This is said to be the-equivalence class of.
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| 8. | The ultraproduct is the set of equivalence classes thus generated.
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| 9. | Then we obtain the following much coarser equivalence class structure.
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| 10. | Every ordered basis lives in one equivalence class or another.
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