Is the sequence given by a Cauchy sequence?
Is the sequence given by a Cauchy sequence?
How many of the following statements are true?
I. If is a Cauchy sequence of rational numbers, then the limit of the is a rational number.
II. If is a Cauchy sequence of irrational numbers, then the limit of the is an irrational number.
III. If is a Cauchy sequence of real numbers, then the limit of the is a real number.
If the sequence is a Cauchy sequence, which of the following must also be Cauchy sequences?
How many of the following statements are true for a sequence of real numbers ?
I. If for a single value of , then is a Cauchy sequence.
II. If for every , then is a Cauchy sequence.