Sentence examples for proofs according to the from inspiring English sources

The article [134] contains several proofs, according to the taste of the several authors.

If one is interested solely in how information from diagrams is situated logically in Euclid's proofs according to the Eu approach, diagrams need not formalized directly as symbols.

More proof: According to the American Bar Association, women in 2008 made up almost half of all associates, but only 18.3percentt of partners.

Another Death in Shooting At Detroit Nightclub Keith Bender, 35, below, who was shot by the rapper Proof, according to the Detroit police, just before Proof himself was shot to death, died of his wounds early yesterday, The Associated Press reported.

The alternative offered by the new rhetoric would furnish a complementary tool to traditional logic, which is limited to the technique of demonstration, or necessary proof according to the rules of deduction and induction; it would add the technique of argumentation.

Proof According to the different location of x i ( 0 ), we deduce it in three cases.

Proof: According to the similarity property of the matrices [38], AB is similar to a Hermitian matrix.

Proof According to the definition of β-dual, it is not too difficult to show that condition (i) holds.

Proof: According to the implicit function theorem [18], a Jacobian matrix must be non-singular at the point of existence.

Proof According to the proof of Lemma 2.1, we can easily obtain local asymptotical stability of w ∗ for ODE system (1.2).

Proof According to the argument in the proof of Theorem 4.1, we see that the initial element x 0 is a mixed ⪯-monotone seed element in X m.