Sentence examples for using the argument used from inspiring English sources

by using the argument used to prove (6.26).

Using similar argument used in the proof of Theorem 3.1 of [11], we can find that the sequence ({x_{n} }) is bounded and Vert x_{n+1}-x_{n} Vert rightarrow0,qquad Vert x_{n}-Tx_{n} Vert rightarrow0,quadtext{as }nrightarrow infty.

Using this theorem, the arguments used in the proof of Theorem 2.4 in [11] can be suitably modified to obtain the following theorem.

Using the same argument used in the first half of the proof for Case I, we get limsup_{n rightarrowinfty} frac{logmax_{1 leq k leq n} X_{k}}{log n} leqepsilonquadmbox{a.s.s

Using the same argument used in the first half of the proof for Case I, we get liminf_{n rightarrowinfty} frac{logmax_{1 leq k leq n} X_{k}}{log n} geqfrac{1}{r}quad mbox{a.s.s

Using the arguments above, we propose to use a robust metric derived in Section 4 to penalize the residual and address the impulsive sampling noise problem.

where does not depend on By using analogous arguments used in Case 1, from (4.13), (4.14) we have (4.15).

Where would we as a society be if one used the argument of not using a public service as the justification for not paying taxes to support it?

"My concern as an Englishman is that they've been used and the argument has been used for narrow political ends in England, first by Margaret Thatcher and now by David Cameron.

Using the same arguments used in proof of Theorem 1, we obtain ∥ y n − x ∗ ∥ ≤ δ θ 1 ∥ x n − x ∗ ∥, Open image in new window.

Harris used the same relativistic argument used by Haeckel and Hitler: because other cultures practice infanticide, we ought to be open to the practice also.