Sentence examples for convergent number from inspiring English sources

Note that any subsequence of a convergent number sequence converges to the same limit.

A convergent number of bacterial hits was found at 3,522 contigs (Fig 7).

The convergent number of pairs in each spacing length decreases as the spacing lengths increase, as happens in co-directional spacing lengths, but the tail is much longer for long distances.

The numbers in the range between this threshold and the preceding number (covering the point of indifference) were presented in a ping-pong style, alternating convergent numbers between high and low depending on the voting behavior.

The result is achieved by the introduction of a new non standard model of Gödel's T, whose new basic objects are pairs of non standard natural numbers (convergent sequences of natural numbers) and moduli of convergence, where the latter are objects giving constructive information about the former.

Proof Using a similar calculation to the one used in the proof of Lemma 4.2, it is not difficult to prove that { x k } is a nonincreasing sequence of nonnegative numbers, hence it is convergent to a number r ∈ R. □.

A sequence ( x k ) (of real or complex numbers) is said to be statistically convergent to some number L if for every ϵ > 0, δ ( { k ∈ N : | x k − L | > ϵ } ) = 0.

A sequence x= (( x_{k} ) ) of complex numbers is said to be statistically convergent to some number ℓ if (delta ( { kin mathbb{N}:vert x_{k}-ell vert geq varepsilon } ) ) has natural density zero for (varepsilon >0).

A sequence x = ( x k ) Open image in new window of numbers is said to be statistically convergent to some number L, in symbol: St − lim x k = L Open image in new window, if for each 휖 > 0 Open image in new window, lim n → ∞ 1 n + 1 | { k ≤ n : | x k − L | ≥ 휖 } | = 0. Open image in new window (2).

A sequence x = (x k ) of numbers is said to be lacunary statistically convergent to a number L (denoted by S θ − lim k → ∞ x k = L Open image in new window) if for each ε > 0, lim r → ∞ 1 h r | { k ∈ I r : | x k − L | ≥ ε } | = 0. Open image in new window.

If a sequence ((x_{n})) is deferred weighted (mathcal{B} -statistically convergent to a numB} -statistically statisticonvergentrred weightod (mathcal{B})-summable to the same number L, buthene converse it not true.