Sentence examples for proof that e from inspiring English sources

In 1873 Hermite published the first proof that e is a transcendental number; i.e., it is not the root of any algebraic equation with rational coefficients.

The proof that E trace H DR H DR H 1 H R H R H H is bounded can be found in [15] or [24].

The proof that E SE ( x ¯ s 2, y ¯ s 2 ) is a saddle point is similar and will be omitted.

Thus, E β a (π c ) ⩾ 0. The proof that E β a (π c ) ⩾ 0 together with γ > (C h − C l ) / P h implies (h, h | h ) ≻ (l, h | h ) is by contradiction.

Some experts said the findings offered no proof that e-cigarettes could harm papers' health.

More studies and research will appear in the years to come to substantiate the claims regarding the benefits of e-cigarettes, but for now, we can go with the current studies, read widely and with an open mind as there is proof that e-cigarettes are a safer alternative than traditional cigarettes.

Proof Let us suppose first that E is ward compact.

Proof It is easy to know that E = C is a Banach space with a maximum norm ∥ ⋅ ∥ and it is also a lattice.

On the other hand, from the proof of Lemma 4.1 we have that E bigl[biglvert u^{varepsilon,tau}(s,x bigrvert ^{2} bigr]leq C< infty for any (s,rgeq0) and (x,yin{mathbb {R}}), which shows that the integrand on the right-hand side of (4.10) is bounded.

Proof Assume that (E) possesses a nonoscillatory solution x ( t ) ∈ N ℓ.

With that we conclude the proof that demonstrates that E i q [ k ] = 0.