Sentence examples for long proof from inspiring English sources

Their immensely long proof made extensive use of a computer, and involved checking more than 1,000 special cases.Another of Mr Casti's five is even older.

Some comments will be helpful for understanding the long proof of Theorem 2.8.

In the following, we will divide the rather long proof into three steps.

(11) See [4], Theorem 4.1, pp.3-4, for a direct (but long) proof of (11) by using the spectral mapping theorem and some existing lemmas.

For the elementary (but long) proof, we refer to  [17, Lemma 2.3].

The mathematician Alan Turing, he noted, had shown long ago that even very short theorems could have very long proofs, running hundreds of pages.

Interestingly, it dates from the same year as the construction, due to Rosser, that eliminates the use of ω-consistency in the first Incompleteness Theorem; like the Speed-up Theorem of Gödel, Rosser's construction exploits the issue of short and long proofs.

The proof was not only noteworthy for its influence on group theory; at 255 pages, it was "possibly the longest proof that had ever been published," says Marcus du Sautoy of the University of Oxford in the U.K., who explained the winners' work at a press conference.

But neither option would be politically sustainable for long without proof of genuine progress.

His study provided gene therapy advocates with what they have long lacked: proof, in principle, that the concept can work.

Justice Madsen, writing for the dissenting justices, said that the First Amendment does not protect false campaign statements, whether or not they injure reputation, as long as proof of actual malice is required.