cauchy sequence meaning in Hindi

Examples

1. In the real numbers every Cauchy sequence converges to some limit.
2. In these cases, the concept of a Cauchy sequence is useful.
3. In metric spaces, one can define Cauchy sequences.
4. In a similar way one can define Cauchy sequences of rational or complex numbers.
5. Clearly, any sequence with a modulus of Cauchy convergence is a Cauchy sequence.
6. In a general metric space, however, a Cauchy sequence need not converge.
7. By definition, in a Hilbert space any Cauchy sequence converges to a limit.
8. The usual decimal notation can be translated to Cauchy sequences in a natural way.
9. Thus one may speak of uniform continuity, uniform convergence, and Cauchy sequences.
10. Cauchy completeness is related to the construction of the real numbers using Cauchy sequences.