Sentence examples for axiom fails from inspiring English sources

Under the present test and housing conditions, this axiom fails to resist the challenge of experimental validation.

In doing so, I was stunned to discover how many of Franklin's axioms failed the acid test of validity and usefulness.

Conventional wisdom dictates selection of a gene that evolves at an appropriate pace for the phylogenetic question of interest, but this axiom often fails to illuminate the correct decision.

But not vice versa: supposing the Axiom of Choice of set theory is true, and that mathematical necessity is unrestricted, a world where the Axiom of Choice fails can be impossible in the first sense without thereby violating any law of our favourite logic.

It's puzzling that we have here two theories of when a sentence is true, and the theories are not equivalent if the axiom of choice fails.

In my book Smart Growth: Building an Enduring Business by Managing the Risks of Growth, I examine those beliefs and find that the Wall Street growth axiom not only fails to describe the behavior of good businesses but causes many to take unnecessary and harmful risks to meet unreasonable expectations.

Then one can show, using the forcing relation between finite approximations to $r$ and formulas in the language of set theory expanded with so-called names for sets in the generic extension, that $M[r]$ is a model of ZFC and $r$ is not constructible in $M[r]$, hence the axiom of constructibility $V=L$ fails.

This model does not satisfy Condition (3), since M3 = also satisfies T; in particular, it satisfies the inertial axiom for f because it fails to satisfy Holds f,s1).

In this place, cars come first in the eyes of the law, and anyone who fails to respect that axiom takes chances in more ways than one.

Though helpfully captioned throughout, "The Hammer" fails to convey the axioms of deaf culture, on which so much of its story depends, thereby missing the opportunity to educate as well as inspire.

The Dutch Book theorem can now be stated: Given a set of betting quotients that fails to satisfy the probability axioms, there is a set of bets with those quotients that guarantees a net loss to one side.