linearly ordered sentence in Hindi
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- Therefore, every nontrivial linearly ordered group is infinite.
- Consider a countable neighborhood basis at, linearly ordered by reverse inclusion with.
- For example, a linearly ordered group that is Archimedean is an Archimedean group.
- The patches of a repository are linearly ordered.
- Because Cantor implicitly assumed that cardinalities are linearly ordered, this case cannot occur.
- One can also glue together different linearly ordered sets to form a circularly ordered set.
- The set of all Dedekind cuts is itself a linearly ordered set ( of sets ).
- Examples of chainable continua include compact connected linearly ordered spaces and in particular closed intervals of real numbers.
- A subset which is-as a sub-poset-linearly ordered, is called a chain.
- Permutations, when considered as arrangements, are sometimes referred to as " linearly ordered " arrangements.
- Thus the example Z above is an example of a GO-space that is not a linearly ordered topological space.
- Every cyclically ordered group can also be expressed as a subgroup of a product, where is a linearly ordered group.
- This result is analogous to Otto H�lder's 1901 theorem that every Archimedean linearly ordered group is a subgroup of.
- The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers.
- In Easton's model, " V " cannot be linearly ordered, so it cannot be well-ordered.
- There are in fact many ways to construct such a linearly ordered set of numbers, but fundamentally, there are two different approaches:
- A convex set is linearly ordered by the cut for any not in the set; this ordering is independent of the choice of.
- For example, given two linearly ordered sets and, one may form a circle by joining them together at positive and negative infinity.
- Every cyclically ordered group can be expressed as a quotient, where is a linearly ordered group and is a cyclic cofinal subgroup of.
- Furthermore, Chang showed that every linearly ordered MV-algebra is isomorphic to an MV-algebra constructed from a group in this way.
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