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The i.i.d. assumption is also used in the central limit theorem, which states that the probability distribution of the sum (or average) of i.i.d. variables with finite variance approaches a normal distribution. [4] The i.i.d. assumption frequently arises in the context of sequences of random variables. Then, "independent and identically ...
The use of LaTeX in a piped link or in a section heading does not appear in blue in the linked text or the table of content. Moreover, links to section headings containing LaTeX formulas do not always work as expected. Finally, having many LaTeX formulas may significantly increase the processing time of a page.
LaTeX (/ ˈ l ɑː t ɛ k / ⓘ LAH-tek or / ˈ l eɪ t ɛ k / LAY-tek, [2] [Note 1] often stylized as L a T e X) is a software system for typesetting documents. [3] LaTeX markup describes the content and layout of the document, as opposed to the formatted text found in WYSIWYG word processors like Google Docs, LibreOffice Writer, and Microsoft Word.
an assumption or subproof assumption. a sentence justified by the citation of (1) a rule of inference and (2) the prior line or lines of the proof that license that rule. Introducing a new assumption increases the level of indentation, and begins a new vertical "scope" bar that continues to indent subsequent lines until the assumption is ...
Therefore, in this article, the Unicode version of the symbols is used (when possible) for labelling their entry, and the LaTeX version is used in their description. So, for finding how to type a symbol in LaTeX, it suffices to look at the source of the article. For most symbols, the entry name is the corresponding Unicode symbol.
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad ...
New details about a study that warned against black plastic spatulas and other kitchen tools have come out. (Getty Creative) (Анатолий Тушенцов via Getty Images)
The above argument works because the exact same reasoning could be applied if the alternative assumption, namely, that the first object is blue, were made, or, similarly, that the words 'red' and 'blue' can be freely exchanged in the wording of the proof. As a result, the use of "without loss of generality" is valid in this case.