Sentence examples for a method of proof from inspiring English sources

He examined propositions by stating possible contradictions and developed the syllogism, a method of proof based on stated premises.

In this paper a method of proof for concurrent systems is presented that combines several approaches to meet the previous goal.

The first was understood as analysis, providing a method of discovery, and the second as synthesis, providing a method of proof.

A predicate calculus is a formal system (a formal language and a method of proof) in which one can represent valid inferences among predications, i.e., among statements in which properties are predicated of objects.

First, it can readily be verified when ω∈ Span(a k)), there holds ( B p ( k ) ( ξ ( k ) ) ⊗ ω ) H V γ = 0 Next for the case of ω∉ Span(a k)), a method of proof by contradiction is adopted.

Analysis came to be seen as a method of discovery, working back from what is ordinarily known to the underlying reasons (demonstrating 'the fact'), and synthesis as a method of proof, working forwards again from what is discovered to what needed explanation (demonstrating 'the reason why').

Further, a method of the proof is also new and interesting, which is to use the mathematical expectation of the distribution function studying the related problems.

Theorem 1.3 appears to be much more general than Theorem 1.1 (obtained by a different method of proof).

This next result is a corollary of the previous Lemma 3.4, but we shall present them using a different method of proof.

Recently, using a similar method of proof to Dubins et al. [2], the present author has proved the following weighted maximal inequality for a standard Brownian motion.

According to Lemma 3.4 and using a similar method of proof as in (3.26), we can obtain the remainder of Theorem 2.1.