Sentence examples for proof to the fact from inspiring English sources

Our results in (ii) provide an alternative proof to the fact that there are n-point metric spaces whose Euclidean distortion is Ω log n).

In Section 2, we first present some definitions and basic results of Stepanov-like type spaces and then we give a short and direct proof to the fact that the space of Stepanov-like weighted pseudo almost periodic functions (respectively Stepanov-like weighted almost automorphic functions) is a Banach space.

We exist as proof to the fact that the simplest activity of buying a shirt can help save a life.

But political experts said she would have a hard time, and as proof, pointed to the fact that Mr. Doggett received over 60percentt of the vote against a Hispanic candidate in the Democratic primary this year.

An Inconvenient Proof refers to the fact that personalization algorithms proselytize via code.

He later argued that he had been coerced under extreme duress to make a false confession; and as proof he pointed to the fact that the details of his confession were at odds with the forensic evidence.

Martin-Löf distinguishes carefully between proofs and derivations: a proof object is a witness to the fact that some proposition has been proved; whereas a derivation is the record of the construction of a proof object.

However, even if my students cannot prove for themselves that atoms and electrons exist, even if they cannot grasp the mathematics of Einstein's proof, I can point them to the fact that the physical world behaves as if our theories about these entities were true.

By standard reasonings as those for the case of classical complex Favard-Szász-Mirakjan operator (see the proof of Theorem 1.8.6 in[3]), combined with those for the Bernstein-Stancu polynomials (see[17] or the proof of Theorem 1.6.5 in[3]), the present proof finally reduces to the proof of the fact that ∥ [ ( α − βz ) f ′ ( z ) + z 2 f ′′ ( z ) ] ( p ) ∥ r > 0 Open image in new window.

We refer the reader to [51] for the proof of the equivalence of (i), (ii), and (iv) and to [60] for the proof of the fact that (i) is equivalent to (iii).

In the case whereT∈A∩C00, this leads to a simple proof of the fact that for everyf∈L1(T) there existsx, y∈H such thatf=xy.