quotient set sentence in Hindi

Examples

1. This distinction gives rise to the notion of a quotient set.
2. Then < " is an equivalence relation; we write for the quotient set.
3. A separable measure space has a natural quotient set can be properly metrized by the induced metric.
4. The quotient set can then be given a structure of the same type, in a natural way, by defining the operations as.
5. For other examples of quotient objects, see quotient ring, quotient space ( linear algebra ), quotient space ( topology ), and quotient set.
6. Using this relation, it is possible to construct a partial order on the quotient set of the equivalence, S / ~, the set of all equivalence classes of ~.
7. If G is a discrete group then a lattice in G is exactly a subgroup \ Gamma of finite index ( i . e . the quotient set G / \ Gamma is finite ).
8. This partition  the set of equivalence classes  is sometimes called the "'quotient set "'or the "'quotient space "'of by and is denoted by.
9. The set of all equivalence classes in with respect to an equivalence relation is denoted as and called "'modulo "'( or the "'quotient set "'of by ).
10. Note that the specific quotient set depends on a choice of maximal torus, but the resulting groups are all isomorphic ( by an inner automorphism of " G " ), since maximal tori are conjugate.