Sentence examples for proof analysis from inspiring English sources

And the second concerns proof analysis, a highly important part of Hilbert's work on Euclidean geometry and geometrical systems generally.

There's also implicit recognition of the requirements of 'finite proof'; this leads us to the second important aspect of the Hilbertian background, namely proof analysis and the use of the Axiom of Choice.

One straightforward kind of proof analysis was designed to reveal what assumptions there are behind accepted 'theorems', and this is clearly pertinent in the case of Zermelo's Axiom of Choice (his sixth axiom) and the WOT.

Unlike a criminal or civil case which impose "beyond a reasonable doubt" and "preponderance of the evidence" standards, respectively, the NFL seemingly has free range in its standard of proof analysis.

HL contributed to study design, proofs, analysis and method implementation; VBY, contributed to study design, proofs, analysis and method implementation; HY contributed source code used for sampling mammal alignments; GAH conceived project, contributed to design, proofs, implementation, analyses and interpretation.

The UN samples will likely offer the final proof, but analysis could take several more weeks.

But until now, we have not found its strict proof of analysis.

In this paper, we will get its strict proof of analysis with the approximation method.

Hilbert thus realized that a direct consistency proof of analysis, i.e., one not based on reduction to another theory, was needed.

In this paper, we will get the strict proof of analysis of a kind of extension of Young inequality with the approximation method.

Feferman and Schütte's proof theoretic analysis of these theories has identified an ordinal (usually referred to as Γ0) which is the least non-predicative ordinal according to this notion.