In case is an -periodic sequence, we say that is an asymptotically -periodic sequence tending to the limit -cycle (This term is introduced since the underlying concept is similar to that of the limit cycle in the theory of ordinary differential equations).
Finally, although the numbers in the sequence tend to the limit 0, they need not actually reach that value.
Cauchy defined an infinitesimal in Cours d'Analyse (1827) in terms of a sequence tending to zero.
Our expectations for HLA allele prediction from exome data were low, because allelic diversity of HLA coding sequence tends to have limited representation in standard capture reagents.
Thus { x n } is non-decreasing sequence tending to x and { y n } a non-increasing sequence tending to y.
Thus, { d ( y n, y n + 1 ) } is a strictly decreasing sequence of positive numbers, and, therefore, tends to a limit r ≥ 0. If possible, suppose that r > 0. Then given δ > 0, there exists a positive integer N such that for each n ≥ N, we have r ≤ d ( y 2 n, y 2 n + 1 ) = d ( T x 2 n + 1, S x 2 n + 2 ) < r + δ, (15).
Thus {d(fx n, fxn+1)} is a decreasing sequence of positive real numbers and, therefore, tends to a limit L. We claim that L = 0.
(3) If (3) tends to a limit as h tends to zero, then that limit is defined as the derivative of f(t), written f′(t).
Therefore, it tends to a limit.
However, for γ > γc, as the system tended to a limit cycle, two phenomena emerged.
If the first ratio tends to a limit strictly over 1, then the second ratio tends either to 1 or to a limit strictly over 1 and in both cases, ρ B tends to a limit strictly over 1.
