Sentence examples for both proofs from inspiring English sources

Both proofs are detailed in Appendix Appendix 3 Proofs of Theorem 2 and Corollary 1. Theorem 2 has been stated in [15]; we provide a complete proof using the O(γ −(t+1+ε)) condition, as well as a proof of the corollary.

If then, fallacious proofs of the contradictory of a thesis depend on their appearing to refute, it is clear that the considerations on which both proofs of false conclusions and an apparent refutation depend must be the same in number.

Both proofs and programs are large formal texts.

However both proofs are technically a bit complicate.

Both proofs use a reduction of the partition problem, an NP-complete problem [21].

Both proofs reveal that when that is, when (Without further assumptions, the regularity of breaks down when ).

Under this null-hypothesis both the proof of equivalence test (E2) and the proof of non-equivalence test (E3) were rejected in about 5% of the simulations, which is the theoretical size of the tests.

They are fascinating as both proof of his craft and as self-analysis.

That diploma is both proof of what he had accomplished and the key to higher learning.

The DIG must work with business partners to rapidly build prototypes for both proof of concept and perfecting through testing.

Both proof of principle and second-generation prototypes are currently being developed in the W.M. Keck Center for Molecular Electronics, in collaboration with Critical Link, LLC of Syracuse, NY.