Sentence examples for by an indirect proof from inspiring English sources

For result (ii), suppose, by an indirect proof, that f is an iterative root of order n ≥ 2 of F on I. Since F ( a ) > a and F ( I ) ⊂ [ b, 1 ], we have, on account of Lemma 2.2, f ( [ b, 1 ] ) ⊂ [ b, 1 ], which shows that f | [ b, 1 ] is a strictly monotonic iterative root of order n ≥ 2 of F | [ b, 1 ].

Nonetheless, the reported 5-year DFS for the sequential arm was judged by many in Europe as an indirect proof of the superiority of this regimen over the classical CMF, thus causing its rapid acceptance as standard treatment for node-positive patients.

To write an indirect proof, you must prove something by finding contradictions of the negation (opposite) of what you need to prove.

This result can also be considered an indirect proof of the agreement between results proposed by Pak and Cho [19] and the mixture model employed in the present article.

This fact could be considered as an indirect proof that primarily financial statements are not presented by the enterprises with the lack of turnover.

Proof For an indirect proof, assume that f : R → R is a C 0 strictly increasing solution of (1.4).

Proof For an indirect proof, assume that f is a C 0 strictly decreasing solution of (1.4).

For result (i), suppose for an indirect proof that there exists t ∗ ∈ [ 0, a ] such that f ( t ∗ ) > a.

No magnetic nanoparticles were observed on the surface of the nanospheres, which is an indirect proof of polymer encapsulation.

Proof For result (i), suppose, for an indirect proof, that f is an iterative root of even order n ≥ 2 of F on I.

It is also an indirect proof showing that the toxic species is indeed related to the aggregation process.