Sentence examples for corresponding statements from inspiring English sources

His development of the pole and polar lines associated with conic sections led to the principle of duality (exchanging "dual" elements, such as points and lines, along with their corresponding statements, in a true theorem produces a true "dual statement") and a dispute over priority with the German mathematician Julius Plücker for its discovery.

The corresponding statements are left to the reader.

These perspectives are complemented by corresponding statements suggesting tasks of professional engineers world-wide.

Naturally, Theorems 1 and 2 are consequences of corresponding statements in Pinto and Kolev (2015c).

This barely scratches the surface and yet already the corresponding statements of wellfoundedness have become less evident.

For μ>0, we hence prove the "if" part of the proposition by exemplarily showing that sup ( r i, p i ) ∈ S i λ T B i r i − μ T p i < ∞ for i=1 as corresponding statements for i=2,…,6 follow along the same lines.

Standard logic includes the "distributive" law, by which a statement of the form "X and either Y or Z" is equivalent to the corresponding statement of the form "Either X and Y or X and Z".

The corresponding statement for triangulated categories is not true.

A corresponding statement is true for operators T, Tn of finite rank which are not necessarily positive.

The problem covers the corresponding statement with p-Laplacian in the principal part, for which it is sufficient to take (mu=0).

We also show that the corresponding statement holds true for the commutant of ˜π(C X)) under the assumption that a certain family of pure states of ˜π(C∗ is total.