Sentence examples for dual statement from inspiring English sources

Sometimes the language of a statement must be modified in order that the corresponding dual statement be clear; the dual of the statement "Two lines intersect in a point" is vague, while the dual of "Two lines determine a point" is clear.

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.

Similarly we can prove the following dual statement.

The dual statement for st- lim inf x can also be proved similarly.

In dual statements released on Monday both the OAIC and Acma outlined that they were aware of the breach, but did not publicly state whether any further investigations would occur.

In the projective geometry of the plane, the words "point" and "line" can be interchanged, giving for example the dual statements: "Two points determine a line" and "Two lines determine a point".

In the projective geometry of the plane, the words "point" and "line" can be interchanged, giving for example the dual statements: "Two points determine a line" and "Two lines determine a point". This last statement, sometimes false in Euclidean geometry, is always true in projective geometry because the axioms do not allow for parallel lines.

Further, the dual statements about the axioms suggest a much more systematic and thoroughgoing duality about a host of other concepts.

The NPI-29 consists of 29 dual statements among which one is considered indicative of narcissism.

Experts say most will be able to execute essential functions, like interbank transfers, but may not be prepared to offer customers extra services, like dual currency statements or other euro-denominated services.

TEHRAN, Iran, Sept. 2 — Iran's leaders issued dual, defiant statements on Sunday, with the president announcing that the nation had 3,000 active centrifuges to enrich uranium and the top ayatollah appointing a new Islamic Revolutionary Guards commander who once advocated military force against students.