Proofs Of Error
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is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the proofs meaning best-known examples of mathematical fallacies, there is some concealment in the presentation of 2=1 proof the proof. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. proof plural There is a striking quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way.[1] Therefore, these fallacies, 1+1=0 proof for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and should not be applied in the cases that are the exceptions to the rules. The traditional way of presenting a mathematical fallacy is to give an invalid step
2=1 Proof Error
of deduction mixed in with valid steps, so that the meaning of fallacy is here slightly different from the logical fallacy. The latter applies normally to a form of argument that is not a genuine rule of logic, where the problematic mathematical step is typically a correct rule applied with a tacit wrong assumption. Beyond pedagogy, the resolution of a fallacy can lead to deeper insights into a subject (such as the introduction of Pasch's axiom of Euclidean geometry[2] and the five color theorem of graph theory). Pseudaria, an ancient lost book of false proofs, is attributed to Euclid.[3] Mathematical fallacies exist in many branches of mathematics. In elementary algebra, typical examples may involve a step where division by zero is performed, where a root is incorrectly extracted or, more generally, where different values of a multiple valued function are equated. Well-known fallacies also exist in elementary Euclidean geometry and calculus. Contents 1 Howlers 2 Division by zero 3 Multivalued functions 4 Calculus 5 Power and root 5.1 Positive and negative roots 5.2 Squaring both sides of an equation 5.3 Square roots of negative numbers 5.4 Complex exponents 6 Geometry 6.1 Fallacy
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Mathematical Fallacies
Password Wrong username or password. Facebook Twitter Google+ Yahoo Remember Me prove 1=0 Forgot password? Register Getour app DictionaryThesaurusMedicalDictionaryLegalDictionaryFinancialDictionaryAcronymsIdiomsEncyclopediaWikipediaEncyclopedia Tools A A A A Language: EnglishEspañolDeutschFrançaisItalianoالعربية中文简体PolskiPortuguêsNederlandsNorskΕλληνικήРусскийTürkçeאנגלית Mobile Apps: apple prove 1+1=3 android For surfers: Free toolbar & extensions Word of the Day Help For webmasters: Free content Linking Lookup box Close proof Also found in: Thesaurus, Medical, https://en.wikipedia.org/wiki/Mathematical_fallacy Legal, Financial, Acronyms, Idioms, Encyclopedia, Wikipedia. proof (pro͞of)n.1. The evidence or argument that compels the mind to accept an assertion as true.2. a. The validation of a proposition by application of specified rules, as of induction or deduction, to assumptions, axioms, and sequentially derived conclusions.b. A statement or argument used in such a http://www.thefreedictionary.com/proof validation.3. a. Convincing or persuasive demonstration: was asked for proof of his identity; an employment history that was proof of her dependability.b. The state of being convinced or persuaded by consideration of evidence.4. Determination of the quality of something by testing; trial: put one's beliefs to the proof.5. Law a. The establishment of the truth or falsity of an allegation by evidence.b. The evidence offered in support of or in contravention of an allegation.6. The alcoholic strength of a liquor, expressed by a number that is twice the percentage by volume of alcohol present.7. Printing a. A trial sheet of printed material that is made to be checked and corrected. Also called proof sheet.b. A trial impression of a plate, stone, or block taken at any of various stages in engraving.8. a. A trial photographic print.b. Any of a limited number of newly minted coins or medals struck as specimens and for collectors from a new die on
Login Help Contact Us About Access You are not currently logged in. Access your personal account or get JSTOR https://www.jstor.org/stable/2005612 access through your library or other institution: login Log in to your https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data/residuals-least-squares-rsquared/v/proof-part-3-minimizing-squared-error-to-regression-line personal account or through your institution. If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for of error your screen reader. Mathematics of Computation Vol. 27, No. 122, Apr., 1973 Simplified Proofs of... Simplified Proofs of Error Estimates for the Least Squares Method for Dirichlet's Problem Garth A. Baker Mathematics of Computation Vol. 27, No. 122 (Apr., 1973), pp. 229-235 Published by: American Mathematical Society DOI: 10.2307/2005612 Stable URL: http://www.jstor.org/stable/2005612 Page Count: 7 Read Online (Free) proofs of error Download ($34.00) Subscribe ($19.50) Cite this Item Cite This Item Copy Citation Export Citation Export to RefWorks Export a RIS file (For EndNote, ProCite, Reference Manager, Zotero…) Export a Text file (For BibTex) Note: Always review your references and make any necessary corrections before using. Pay attention to names, capitalization, and dates. × Close Overlay Journal Info Mathematics of Computation Description: This journal, begun in 1943 as Mathematical Tables and Other Aids to Computation, publishes original articles on all aspects of numerical mathematics, book reviews, mathematical tables, and technical notes. It is devoted to advances in numeri cal analysis, the application of computational methods, high speed calculating, and other aids to computation. Moving Wall Moving Wall: 5 years (What is the moving wall?) Moving Wall The "moving wall" represents the time period between the last issue available in JSTOR and the most recently published issue of a journal. Moving walls are generally represented in years. In rare instances, a publisher has elected to have a "zero" moving wall, so their current issues are avai
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