Sentence examples for whence we deduce from inspiring English sources

Whence we deduce that 1 ≤ α ¯ ( 1, 1 ) < 1, which provides a contradiction.

Whence we deduce that the partial quasi-metricspace ( Σ c, k ∞, q B ) is complete.

Since θ < 1, it follows that the right-hand side of the above inequality tends to zero as n → ∞, whence we deduce that u n → u as n → ∞.

Whence we deduce, by Remark 19, that f T Q ∈ Θ ( n 2 ), which is in accordance with the Quicksort (worst case behavior) asymptotic complexity class that can be found in the literature [44, 45].

By Theorem 9 we obtain v h ⊑ s p w. Whence we deduce that h ≤ f w and, hence, that f w ∈ Ω ( h ) or, equivalently, that f T ∈ Ω ( h ).

Since v ⊑ s p Φ z ( v ) we deduce that q B ( v, Φ z ( v ) ) = 0. Hence, by assertion (2) in statement of Lemma 8, wefind that q B ( v, w ) = 0. Whence we deduce that v ⊑ s p w.

Whence we immediately deduce that the function α ¯ holds all the requirements in Definition 12, i.e., θ ( a, b ) < 1 for every 0 ≤ a ≤ b.

Let, where, we deduce (5.12).

Clearly, (6) and (19) are equivalent, whence we derive the statement concerning the uniqueness of ψ. □.

Whence, by Theorem 11, we deduce that f has a unique fixed point.

Can we deduce from the comments that the best choice would be Jim's?