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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 legal term probity means authority or credibility, the power of testimony to prove facts when given by persons of reputation or status. [6] Plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof. [7]
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 length of unusually long proofs has increased with time. As a rough rule of thumb, 100 pages in 1900, or 200 pages in 1950, or 500 pages in 2000 is unusually long for a proof. 1799 The Abel–Ruffini theorem was nearly proved by Paolo Ruffini , but his proof, spanning 500 pages, was mostly ignored and later, in 1824, Niels Henrik Abel ...
Even though equivalence relations are as ubiquitous in mathematics as order relations, the algebraic structure of equivalences is not as well known as that of orders. The former structure draws primarily on group theory and, to a lesser extent, on the theory of lattices, categories , and groupoids .
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This is a list of abbreviations used in law and legal documents. It is common practice in legal documents to cite other publications by using standard abbreviations for the title of each source. Abbreviations may also be found for common words or legal phrases.
Many circuit courts have said that law enforcement can hold your property for as long as they want. D.C.’s high court decided last week that’s unconstitutional.