Sentence examples for continuing this manner from inspiring English sources

Continuing this manner we can define a sequence as follows: (2.3).

Now let (J_3) be a cyclic right ideal contained in (J_2) and by continuing this manner we have a descending chain (J_1 ge J_2 ge cdots ) of right ideals of (D) where for each odd integer (i), (J_i) is cyclic and for each even integer (i), (J_i) is not cyclic.

In the next round, the winners again debate in groups of two the merits of the proposals, continuing in this manner until a winner emerges.

Continuing in this manner, take the previous divisor (8), divide it by the previous remainder (4), and write the result as 8 = 2 × 4 + 0.

Continuing in this manner, we get (14).

Continuing in this manner, we can obtain (5.15).

Continuing in this manner, we can obtain A : = ⋂ i = 1 r A i ≠ ∅.

Continuing in this manner, we get (f^{n} x_{0} in X_{0}) for every (n geq1).

By continuing in this manner we have a descending chain ( S oplus M ge Soplus M_1 ge S oplus M_2 ge cdots ) of submodules of (S oplus M).

Continuing in this manner, data injected by source node-3 to its first path reaches the base station without being split into multiple branches.

Continuing in this manner one can show that there are many strongly inaccessibles below κ and, in fact, that κ is Mahlo, indescribable, ineffable, etc.