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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 Germany, file sharing of copyrighted files, for example through peer-to-peer software like BitTorrent, is illegal. Internet service providers routinely transmit the identity of IP address owners to private lawyer firms who are then able to send "cease and desist" letters often demanding the offender to pay €1,000 fines or more.
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
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A rare gold coin was donated to a Salvation Army Red Kettle in Washington, Pennsylvania, by an anonymous good Samaritan due to holiday foot traffic. Coin expert weighs in.
You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.
Whereas the notion of "free equivalence relation" does not exist, that of a free groupoid on a directed graph does. Thus it is meaningful to speak of a "presentation of an equivalence relation," i.e., a presentation of the corresponding groupoid;