Sentence examples for equivalent the sequence from inspiring English sources

Then the following are equivalent: The sequence { x n } is G-Cauchy.

Then the following are equivalent: (1) The sequence (x n ) is a G-Cauchy sequence.

The following statements are equivalent: (1) The sequence { x n } is G-Cauchy.

The following statements are equivalent: (A) The sequence ({x_{n}}) is Cauchy in ((X, q)).

Then the following are equivalent: (1) The sequence { x n } is G b -Cauchy.

Hence (24) has at least one solution asymptotically equivalent to the sequence ((prod_{i=1}^{n}p_{i} ) = sqrt{n+1}).

Hence, (25) has at least one solution asymptotically equivalent to the sequence ((prod_{i=1}^{n}p_{i} ) equiv1).

In the equivalent set, the sequence which has the least swap operator is called basic swap sequence of the set or basic swap sequence (BSS) in short.

If X is a G-metric space, then the following are equivalent: (a) The sequence {x n } is G-Cauchy.

In a G-metric space ( X, G ), the following are equivalent: (i) The sequence { x n } is G-Cauchy.

However, the two notions are equivalent provided the sequence {S n }n∈ℕis equicontinuous when the domains of definitions are identical.