Sentence examples for yields the assertion from inspiring English sources

Exact(10)

So making k → ∞, (3.4) yields the assertion.

This immediately yields the assertion by letting t → ∞ in the previous inequality.

end{aligned} Inserting this bound into (19) (which holds for arbitrary (v_{h})) yields the assertion.

Now summing over all facets (F_{T} inmathbb{F}_{T}) yields the assertion.

Thus, we have ∑ n = 2 ∞ d n | a n | r n − p < ( B − A ) a p, which, upon letting r → 1 −, readily yields the assertion (15).

So, ω φ λ 2 r ( f, t ) ≤ C ( h α + ( t h ) 2 r ω φ λ 2 r ( f, h ) ), which yields the assertion of Theorem 2 by the Berens-Lorentz lemma.

Show more...

Similar(50)

Analogous argument yields the second assertion.

Applying the Chebyshev inequality yields the required assertion.

It yields the desired assertion (P(E_{i2}capOmega_{i2})=0) immediately.

It yields the desired assertion (mathbb{P}(J_{2}cap E_{2})=0) immediately.

To proceed, applying the Chebyshev inequality yields the required assertion.

Show more...

Ludwig, your English writing platform

Write better and faster with AI suggestions while staying true to your unique style.

Student

Used by millions of students, scientific researchers, professional translators and editors from all over the world!

MitStanfordHarvardAustralian Nationa UniversityNanyangOxford

Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak quote

Justyna Jupowicz-Kozak

CEO of Professional Science Editing for Scientists @ prosciediting.com

Get started for free

Unlock your writing potential with Ludwig

Letters

Most frequent sentences: