Sentence examples for be two convergent sequences from inspiring English sources

Let be two convergent sequences with the same limit, then is said to converge faster than (see, e.g., [5]) if (2.1).

Now, let ( a k ) and ( b k ) be two convergent sequences of nonzero real numbers with lim k → ∞ a k = a and lim k → ∞ b k = b ≠ 0. (1).

This shows that and are two convergent sequences of numbers.

This shows that and are two convergent sequences of numbers by the boundedness of.

From (3.2) we see that and are two convergent sequences of numbers.

A mapping F : X × X → X is said to be continuous if for any two convergent sequences { x n } and { y n } converging to x and y in X, respectively, then { F ( x n, y n ) } is convergent to F ( x, y ).

After showing convergence in probability for the sum of two convergent sequences, scalar product and product of two sequence, we will show that each continuous function of convergent in probability sequence is convergent in probability.

Suppose { a n } and { b n } are two real convergent sequences with limits a and b, respectively.

Definition 1. [4] Suppose that {a n } and {b n } are two real convergent sequences with limits a and b, respectively.

Let fix x0 ∈ X and let y n n = 1 ∞ and z n n = 1 ∞ be two sequences, that are convergent to x0.

Especially, it has the property that differentiates it from other spaces, that is, the self-distance of any point may not be zero, also a convergent sequence need not have unique limit in these spaces.