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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 ...
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".
The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
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]
In most disciplines, evidence is required to prove something. Evidence is drawn from the experience of the world around us, with science obtaining its evidence from nature, [11] law obtaining its evidence from witnesses and forensic investigation, [12] and so on. A notable exception is mathematics, whose proofs are drawn from a mathematical ...
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 computation of time by civil reckoning is the rule, and it comes into application where the acquisition of a right depends upon the lapse of a certain time, in which case any hour or moment of the day suffices; however, where the loss of a right depends upon lapse of time, the last day must have wholly expired. [4]
In this theory, a system is called "holonomic" if, in a certain sense, one can recover global information from local information, so the meaning "entire-law" is quite appropriate. The rolling of a ball on a table is non-holonomic, because one rolling along different paths to the same point can put it into different orientations.