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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 ...
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 ...
In a legal dispute, one party has the burden of proof to show that they are correct, while the other party has no such burden and is presumed to be correct. The burden of proof requires a party to produce evidence to establish the truth of facts needed to satisfy all the required legal elements of the dispute.
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]
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 .
Another selfie was in the same spot but with a little more festive flair. The star posed with a kissy face while wearing an oversized Grinch shirt.
In 2024, the wide, wide world of sports saw repeat champions, first-time titlists, a grand Paris summer and some epic fails. The winners and losers:
An offer of proof is a kind of motion that a lawyer may present to a judge or to the official presiding over a hearing. It is an explanation made by an attorney to a judge during trial to show why a question which has been objected to as immaterial or irrelevant will lead to evidence of value to proving the case of the lawyer's client.