| 1. | Therefore, every nontrivial linearly ordered group is infinite.
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| 2. | Consider a countable neighborhood basis at, linearly ordered by reverse inclusion with.
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| 3. | For example, a linearly ordered group that is Archimedean is an Archimedean group.
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| 4. | The patches of a repository are linearly ordered.
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| 5. | Because Cantor implicitly assumed that cardinalities are linearly ordered, this case cannot occur.
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| 6. | One can also glue together different linearly ordered sets to form a circularly ordered set.
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| 7. | The set of all Dedekind cuts is itself a linearly ordered set ( of sets ).
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| 8. | Examples of chainable continua include compact connected linearly ordered spaces and in particular closed intervals of real numbers.
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| 9. | A subset which is-as a sub-poset-linearly ordered, is called a chain.
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| 10. | Permutations, when considered as arrangements, are sometimes referred to as " linearly ordered " arrangements.
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