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The outlines described in this article are lists, and come in several varieties. A sentence outline is a tool for composing a document, such as an essay, a paper, a book, or even an encyclopedia. It is a list used to organize the facts or points to be covered, and their order of presentation, by section.
Abstract is often expected to tell a complete story of the paper, as for most readers, abstract is the only part of the paper that will be read. It should allow the reader to give an elevator pitch of the full paper. [19] An academic abstract typically outlines four elements relevant to the completed work:
In 1978 Wilhelm Klingenberg published a proof that smooth compact manifolds without boundary have infinitely many closed geodesics. His proof was controversial, and there is currently (as of 2016) no consensus on whether his proof is complete. In 1991, Kapranov and Voevodsky published a paper claiming to prove a version of the homotopy hypothesis.
Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the n th triangular number. In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.
If no proof is offered (in either direction), then the proposition can be called unproven, undecided, inconclusive, an open problem or a conjecture. In debates, appealing to ignorance is sometimes an attempt to shift the burden of proof. The term was likely coined by philosopher John Locke in the late 17th century. [3] [4]
A post on X claims that Tesla CEO Elon Musk once stated that instead of ending world hunger, he would focus on “making life harder for trans people.” Verdict: False There is no proof that he ...
The beginning of a proof usually follows immediately thereafter, and is indicated by the word "proof" in boldface or italics. On the other hand, several symbolic conventions exist to indicate the end of a proof. While some authors still use the classical abbreviation, Q.E.D., it is relatively uncommon in modern mathematical texts.
A Honduras gang member who was illegally in the US “giggled” as he admitted kidnapping a young Texas woman at gunpoint and threatening to pimp her out and sell her organs, according to cops.