Sentence examples for proof of equality from inspiring English sources

The proof of equality (4) is similar to the proof of equality (3).

Step 2. In the general case, when (16) holds, the proof of equality (24) is more complicated, so we only outline the main ideas.

end{aligned} (41) As we have already shown in the proof of equality (28), the lateral boundary condition implies T_{, 3}=0,qquad T_{, alpha}=n_{alpha}frac{partial T}{partial n}, on the curve (partial D x_{3})).

Similar to the proof of equality in inequality (4.6), we easily know that equality holds in (4.7) if and only if (overline{nabla}^{tau}_{p} K=overline{nabla}^{-tau}_{p} K) when (tauneq0).

By Theorem 1, ψ p ( x ) ∈ H f and equality (6), we obtain R i m ( F n ( x ) ) = F n ( R i m ( x ) ) = lim p → ∞ F n ( R i m ( ψ p ( x ) ) ) = lim p → ∞ 1 i n − i m F n ( ψ p ( x ) ) = 1 i n − i m F n ( x ). for all n, m ∈ Z, n ≠ m, x ∈ H. (iii) The proof of equality (4) is similar to the proof of equality (3).

Since the proof of each equality uses the same method, we give the proof for only last three equalities.

Swingle, B. & Senthil, T. Geometric proof of the equality between entanglement and edge spectra.

The success of individual blacks is seen as proof of racial equality, while, as Mr. McKnight writes, "the exceptional white racist is used to separate the existing racial white community from the onus of the past practices of Jim Crow".

The proof of the equality (1.1a).

A simple proof of the equality can be done by performing an integration by parts in the integrals from the right side and changing the variable.

The establishment of the democracy was to radically change Athens:"And so it was that the Athenians found themselves suddenly a great power...they gave vivid proof of what equality and freedom of speech might achieve".