Sentence examples for whence by from inspiring English sources

Thus, and it belongs to, whence by Lemma 2.3(c).

Whence, by Theorem 11, we deduce that f has a unique fixed point.

whence by Theorem 8 we have that H [ G 0 ] = G 0. The desired conclusion (ii) then directly follows by comparing the entries in the above equality.

In the presence of constant symbols, classical quantificational logic allows us to derive the sentence $\exists x \ a = x$ as a theorem, whence, by necessitation for complete sentences, we infer $\Box \exists x \ a= x$, which seems objectionable if $a$ is suppose to regiment a name for an object that exists only contingently.

Whence, by the induction hypothesis, we infer that f | [ a k, a k − 1 ] ∘ f | [ a k − 1, a k − 2 ] ∘ ⋯ ∘ f | [ a, a − 1 ] ∘ f | [ a − 1, a ∗ ]. is strictly increasing, i.e. f k + 2 | [ a − 1, a ∗ ] is strictly increasing.

Notice that for B ∈ ( − 1, 0 ] the function on the right hand side of (2.13) maps the open unit disc onto the disc D ( C, R ) = { w ∈ C : | w − C | < R }, where C = B ( A − B ) 1 − B 2, R = | A − B | 1 − B 2. This function is also univalent in whence, by (1.1), Theorem 2.3 can be written in the following form.

IV, whence ¬!∩ by ARD2, whence ¬(U → ∩) by ARD1, whence ¬(U → (U → ∩)) by R, whence ¬(U → !∩) by ARD1, whence Axiom V by Def.

On February 1 , 2015 on the occasion of the Super Bowl, the people at Carnival Corporation aired an advertisement with a recording of that speech, to encourage Americans to return "from whence we came," by which, I assume, they mean an unlimited prime-rib buffet.

These days, the word "authentic" is synonymous with "sounds like", so yes, he's authentic, with the caveat that authentic should really mean "true to the era whence it sprang", by which measure the most authentic 21st-century music would be the sound of MP3s bleeping or digital bytes going whrrrrr.

whence it follows, by taking limits, that (2.16).

whence we obtain by computation that ∫ 0 T 2 α ¯ 2 ( t ) d t = T 3 80.