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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 ...
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 >.
In law, a test is a commonly applied method of evaluation used to resolve matters of jurisprudence. [1] In the context of a trial , a hearing , discovery , or other kinds of legal proceedings , the resolution of certain questions of fact or law may hinge on the application of one or more legal tests.
Ravel Law is a startup which offers free access to computer-assisted legal research. The firm has funded a major scanning project at the Harvard Law School library known as "Free the Law". The project aims to have the full collection of 40 million pages digitized by 2017. [ 1 ]
(Note that, by property 1, the local holonomy group is a connected Lie subgroup of G, so the adjoint is well-defined.) The local holonomy group is not well-behaved as a global object. In particular, its dimension may fail to be constant. However, the following theorem holds:
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 ...
For example, we can prove by induction that all positive integers of the form 2n − 1 are odd. Let P ( n ) represent " 2 n − 1 is odd": (i) For n = 1 , 2 n − 1 = 2(1) − 1 = 1 , and 1 is odd, since it leaves a remainder of 1 when divided by 2 .
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. [1]