Sentence examples for contradiction 1 from inspiring English sources

There are three facts about the New York City subway that, when taken together, seem to lead to a contradiction: 1.

If there is a subsequence ( c n k ) k ∈ N ∗ → ∞, the choice ε = ε k = ( 1 + b ) c n k leads to the contradiction 1 ≤ a ( 1 + b ) α ψ ( ε k ) → 0. Therefore, the sequence ( c n ) is bounded.

Note that x 0 ≠ 0. Otherwise, we would obtain the following contradiction: 1 ≥ lim inf n ∥ x n ∥ = lim inf n ∥ x 0 + x n ∥ > σ − ε > a ≥ 1.

If we accept the aforementioned Law of Bivalence, that is, the principle according to which all sentences are either true or false, both alternatives lead to a contradiction: (1) is both true and false, that is, a dialetheia, contrary to the LNC.

(13) From (12) and (13), we have the following contradiction: 1= Vert tilde{u}_{alpha_{n}} Vert + Vert tilde{v}_{alpha_{n}} Vert leq biglVert tilde{u}_{alpha_{n}}^ bigrVert + biglVert tilde{v}_{alpha_{n}}^ bigrVert + biglVert tilde{u}_{alpha_{n}}^ bigrVert + biglVert tilde{v}_{alpha_{n}}^ bigrVert to0 as (ntoinfty).

Hence, we have the contradiction ρ1 = ρ2.

If, we shall have a contradiction: (2.4).

Letting, we obtain the contradiction (3.5).

If, we reach the following contradiction: (3.22).

By Definition 2.1 this yields a contradiction (3.42).

For, by (3.6) we have the following contradiction: (3.16).