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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 ...
The well-definedness condition corresponds to the requirement that every infinite path must eventually pass through a sufficiently long node: the same requirement that is needed to invoke a bar induction. The principles of bar induction and bar recursion are the intuitionistic equivalents of the axiom of dependent choices. [3]
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 >.
The examples and perspective in this article deal primarily with common law countries, particularly the United States, and do not represent a worldwide view of the subject. You may improve this article , discuss the issue on the talk page , or create a new article , as appropriate.
Hence the functional calculus is well-defined. Consequently, if f 1 and f 2 are two holomorphic functions defined on neighborhoods D 1 and D 2 of σ(T) and they are equal on an open set containing σ(T), then f 1 (T) = f 2 (T). Moreover, even though the D 1 may not be D 2, the operator (f 1 + f 2) (T) is well-defined.
If you've been having trouble with any of the connections or words in Saturday's puzzle, you're not alone and these hints should definitely help you out. Plus, I'll reveal the answers further down
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 ...
“Kansas did that 10 years ago,” said Schwab, a Republican. “It didn’t work out so well.” Steven Fish, a 45-year-old warehouse worker in eastern Kansas, said he understands the motivation behind the law. In his thinking, the state was like a store owner who fears getting robbed and installs locks.