Sentence examples for proof reveals from inspiring English sources
So Einstein's proof reveals why the Pythagorean theorem applies only to right triangles: they're the only kind made up of smaller copies of themselves.
A careful examination of the proof reveals the fact that Theorem 2.1 (hence also Corollary 2.1) remains valid in symmetric space (X, d) wherein d is continuous.
If we consider any finite group of data points, an elementary proof reveals that there are an infinite number of distinct mathematical functions describing different curves that will pass through all of them.
From signatures on Securities and Exchange Commission filings to his own sworn testimony, this body of proof reveals how Romney's fingerprints lingered on Bain transactions well into 2002, even while he was managing the Olympics.
Remark 3.2 The proof reveals that the efficiency estimate (3.4) is valid for any approximation ϕ h of ϕ, while the upper reliability estimate (3.5) requires some Galerkin orthogonality.
In fact, an inspection of their proof reveals that their algorithm is O(n d3 τ Bell, where d is the maximum degree of the tree. Bell(k) denotes the kth Bell number, which is the number of unordered partitions of k items; these numbers are known to satisfy the bounds k e In k k < Bell k < k In k k [ 7].
SCHOOL COMPLETION -- Concerning the first output, school completion, the proof revealed that of those New York City ninth graders who do not transfer to another school system, only 50percentt graduate in four years, and 30percentt do not graduate or receive a general equivalency degree... by the age of 21, when they cease to be eligible for free public education.
There's documented proof revealing an actual, real world conspiracy funded by oil and coal companies to mislead the public.
An analysis of Liu's proofs reveals some recurring procedures.
Both proofs reveal that when that is, when (Without further assumptions, the regularity of breaks down when ).
Second, a general mathematical theory sheds much more light on the underlying mechanisms, since the proofs reveal the role that various assumptions play in yielding the conclusions.
