Sentence examples for for a proof by from inspiring English sources

For a proof by contradiction, assume this is not the case.

For a proof by induction, we assume that | γ j | ≤ C j e K ( j − 1 ), j ≤ n − 1.

For a proof by contradiction, assume a Nash equilibrium pricing point where (D(P)> S_{i}^{(max)}) and p i is the lowest price.

For result (ii), we will give a proof by contradiction.

We next looked for a proof of the existence of birhythmicity by analyzing the first return map from and to the boundary between the domains D14 and D24 ([0, x) axis in Figure 10) which is crossed by both oscillatory regimes.

By an example, however, we show that their result is not correct and so we give the correct form of it applying a new method for its proof, by establishing a separation theorem.

For additional proof by immunoelectron microscopy, an Escherichia coli expressed, His-tagged HEV genotype 3 capsid protein derivative harboring amino acid residues 326 608 (11 ) was used to generate HEV-positive serum in a rabbit by 3 subcutaneous inoculations at 4-week intervals (P. Dremsek et al., unpub. data).

For completeness, here we give a different proof by following the proof.

The White House, struggling to defend Trump's allegation, deflected requests for proof by calling on Congress to investigate.

Now to prove this, assume both *13·01 and the Axiom of Reducibility, and suppose, for proof by reductio, that x = y, and φx, and not φy, for some function φ of arbitrary type.

As an application, we give a proof for the claim by Bajpai et al. that the bilateral series (B(f q)) of the third order mock theta function (f q)) is a mixed mock modular form.