Assume contrarily, that is, x ≠ v. Since lim n → ∞ d ( x n, v ) exists (by Lemma 2.1), therefore by the uniqueness of asymptotic centers, we have lim sup n → ∞ d ( v n, v ) < lim sup n → ∞ d ( v n, x ) ≤ lim sup n → ∞ d ( x n, x ) < lim sup n → ∞ d ( x n, v ) = lim sup n → ∞ d ( v n, v ), a contradiction.
Assume contrarily, that is, x ≠ v. Since lim n → ∞ d ( x n, v ) exists by Lemma 3.1, therefore, by the uniqueness of asymptotic centers, we have lim sup n → ∞ d ( y n, v ) < lim sup n → ∞ d ( y n, x ) ≤ lim sup n → ∞ d ( x n, x ) < lim sup n → ∞ d ( x n, v ) = lim sup d ( y n, v ), a contradiction and hence x = v.
To the Communists, Coca-Cola may be a drink that has sinister Catholic connections, but at least one Catholic newspaper has suggested, contrarily, that Mohammed is the Prophet not only of Allah but of Cocah-Colah, too.
I tend to think, contrarily, that the two parts of a double wave are actually broken pieces of the same wave — one that has been refracted in its sweep along the coast in such a way that one section has slipped behind the other and run up on its back.
Assume contrarily that (zin F(T^{n})) and (znotin F(T)).
In order to prove (ii), we suppose contrarily that δ ( 0, G ) = 1 and seek a contradiction.
Contrarily, articles that reported prevalence and incidence data on CVD risk and/or articles that report on CVD risk-related beliefs and behaviors were included.
Contrarily, suppose that, then, (3.25).
Contrarily to that "one pot" syntheses, majority of previously published synthesis routes to titania photocatalysts are multi-step processes employing metal alkoxides as raw materials, non-aqueous solvents, and/or including crystallization step after chemical synthesis of precursors.
Contrarily, those that require a major change in clinical or public health protocols, for example, the initiation of a universal screening program, cannot fulfill their potential until such changes are established.
Contrarily, suppose that there exists some such that, that is, (3.19).
