Search results
Results from the WOW.Com Content Network
Questions regarding the well-definedness of a function often arise when the defining equation of a function refers not only to the arguments themselves, but also to elements of the arguments, serving as representatives. This is sometimes unavoidable when the arguments are cosets and when the equation refers to coset representatives. The result ...
The legal term probity means authority or credibility, the power of testimony to prove facts when given by persons of reputation or status. [6] Plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof. [7]
Depending on the type of singularity in the integrand f, the Cauchy principal value is defined according to the following rules: . For a singularity at a finite number b + [() + + ()] with < < and where b is the difficult point, at which the behavior of the function f is such that = for any < and = for any >.
As a result, once a proof is given for the particular case, it is trivial to adapt it to prove the conclusion in all other cases. In many scenarios, the use of "without loss of generality" is made possible by the presence of symmetry. [2]
Spinoza's original text of Ethics, Part 1, Q.E.D. is used at the end of Demonstratio of Propositio III on the right hand page Perhaps the most famous use of Q.E.D. in a philosophical argument is found in the Ethics of Baruch Spinoza , published posthumously in 1677. [ 11 ]
Relevance, in the common law of evidence, is the tendency of a given item of evidence to prove or disprove one of the legal elements of the case, or to have probative value to make one of the elements of the case likelier or not. Probative is a term used in law to signify "tending to prove". [1] Probative evidence "seeks the truth".
In law, knowledge is one of the degrees of mens rea that constitute part of a crime.For example, in English law, the offence of knowingly being a passenger in a vehicle taken without consent requires that the prosecution prove not only that the defendant was a passenger in a vehicle and that it was taken by the driver without consent, but also that the defendant knew that it was taken without ...
Using the full AC, one can well-order the formulas, and prove the uncountable case with the same argument as the countable one, except with transfinite induction. Other approaches can be used to prove that the completeness theorem in this case is equivalent to the Boolean prime ideal theorem, a weak form of AC.