Sentence examples for a complete proof for from inspiring English sources

Here we give a complete proof for the reader's convenience.

Now, we will provide a complete proof for some of results obtained in this and the following sections so that the reader may be familiar with the ways the proofs are constructed and written.

Harvard mathematics professor Shing-Tung Yau, winner of the Fields Prize, said the excellent job done by Zhu and Cao was the final strike on a global collaborative work for a complete proof.

When S is the adjacency matrix, (2) is a relaxation of maximizing the ratio association; when S is the normalized adjacency matrix, (2) is a relaxation of minimizing the normalized cut [13] (see Appendices A, B for a complete proof).

In particular, our result contains a 2H rmax -approximation algorithm for ECP, which gives an independent and complete proof for the result first obtained by Jain et al. (Proceedings of the SODA, 1999, p. 484–489).

So, the main purpose of this paper is to overcome those shortcomings and present complete proofs for Ouyang et al. (2006).

So, this paper will use calculus to explore and adopt the convexities of the total annual relevant costs to overcome those drawbacks and present accurate and complete proofs for Theorems 1 and 2 in Ouyang et al. (2006).

For a sound and complete proof system for logic with an empty domain, see (Tennant 1990).

Priest (1992) gives a sound and complete proof theory for the given semantics, but this is left for the reader to consult.

That there is a sound and complete proof procedure for FO was first proven by Kurt Gödel (1930).

\ \text{PHP}_n\) is hence provable in any complete proof system for propositional logic.