Sentence examples for proof failed from inspiring English sources

As formulated by Field, the proof failed to address the crucial case of actual applications of mathematics.

I mean the possible world which is minimally different from the actual world in which....) Conditional Proof fails for Stalnaker's semantics.

After examining the calculations in the proof of the uniqueness part in Theorem 8 in [1] and Steps 3 and 4 of Theorem 16, we found that they do not lead to strict inequalities, and hence the proofs failed.

Here we propose reasoned modelling critics — an approach which aims to abstract away from the complexities of low-level proof obligations, and provide high-level modelling guidance to designers when proofs fail.

For Hilbert, the aims were a complete clarification of the foundational problems through finitary proofs of consistency, etc, aims in which proof theory failed.

Firstly, we point out that Dalal et al. [31] used the completeness of X in their proof but failed to mention the same in the hypotheses.

Although Ernst Zermelo demonstrated less than a day later that König's proof had failed, Cantor remained shaken, and momentarily questioning God.

Antibiotics that were once thought to be evolution proof have failed to live up to their promises (Perron et al. 2006; Sun et al. 2009b).

They assigned the burden of proof to the IAAF – and the party which has the burden of proof usually fails.

He tries several times to find proof, but fails.

This proof often fails in living systems for two main reasons: First, periods of synchronization are naturally very short, and consequently testing for deterministic phase relations is not appropriate.