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In particular, the term well-defined is used with respect to (binary) operations on cosets. In this case, one can view the operation as a function of two variables, and the property of being well-defined is the same as that for a function. For example, addition on the integers modulo some n can be defined naturally in terms of integer addition.
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 ...
The result of the procedure for principal value is the same as the ordinary integral; since it no longer matches the definition, it is technically not a "principal value". The Cauchy principal value can also be defined in terms of contour integrals of a complex-valued function f ( z ) : z = x + i y , {\displaystyle f(z):z=x+i\,y\;,} with x , y ...
In the IRAC method of legal analysis, the "issue" is simply a legal question that must be answered. An issue arises when the facts of a case present a legal ambiguity that must be resolved in a case, and legal researchers (whether paralegals, law students, lawyers, or judges) typically resolve the issue by consulting legal precedent (existing statutes, past cases, court rules, etc.).
While for the definition via intersection well-definedness hinges only on the property that intersections of fields are themselves fields, here two auxiliary assertion are included. That 1. there exist minimal subfields of K that include E 1 {\displaystyle E_{1}} and E 2 {\displaystyle E_{2}} and 2. that such a minimal subfield is unique and ...
To set up the casebook method of law study, American law professors traditionally collect the most illustrative cases concerning a particular area of the law in special textbooks called casebooks. Some professors heavily edit cases down to the most important paragraphs, while deleting nearly all citations and paraphrasing everything else; a few ...
For example, direct proof can be used to prove that the sum of two even integers is always even: Consider two even integers x and y. Since they are even, they can be written as x = 2a and y = 2b, respectively, for some integers a and b. Then the sum is x + y = 2a + 2b = 2(a+b). Therefore x+y has 2 as a factor and, by definition, is even. Hence ...
In modern constitutional law, the rational basis test is applied to constitutional challenges of both federal law and state law (via the Fourteenth Amendment).This test also applies to both legislative and executive action, whether those actions be of a substantive or procedural nature.