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Extraneous and missing solutions information


In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it.[1] A missing solution is a valid one which is lost during the solution process. Both situations frequently result from performing operations that are not invertible for some or all values of the variables involved, which prevents the chain of logical implications from being bidirectional.

  1. ^ Ron Larson (1 January 2011). Calculus I with Precalculus. Cengage Learning. pp. 4–. ISBN 978-0-8400-6833-0.

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Extraneous and missing solutions

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an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. A missing solution...

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Equation solving

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integration.[citation needed] Solutions of differential equations can be implicit or explicit. Extraneous and missing solutions Simultaneous equations Equating...

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Solution set

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E=\{e^{ix}=1\}} with respect to x ∈ C {\displaystyle x\in \mathbb {C} } is S = 2πZ (see Euler's identity). Equation solving Extraneous and missing solutions...

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Voynich manuscript

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f71r, f72v1, f72v3 and f73r. Every page in the manuscript contains text, mostly in an unidentified language, but some have extraneous writing in Latin script...

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Enigma Variations

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but the work may be listened to as a 'piece of music' apart from any extraneous consideration. In naming his theme "Enigma", Elgar posed a challenge which...

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Death on the Nile

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earth, and you scrape here and there with a knife until finally your object is there, all alone, ready to be drawn and photographed with no extraneous matter...

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Rational planning model

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control and who acts only after carefully weighing all options, the Rational Actor method allows scholars to filter out extraneous details and focus attention...

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Interactive voice response

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however, the user is likely to include extraneous words or phrases (e.g. "I was just looking at my bill and saw that my balance was wrong."). The open-ended...

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Pentium F00F bug

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memory containing the descriptor for the undefined-opcode exception. These extraneous memory accesses turned out to be sufficient for the bus interface to let...

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Fermentation theory

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Pasteur used the same flasks and sugar-yeast mixture, but left it idle in 'swan-neck' flasks instead of introducing any extraneous matter. Some flasks were...

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Hydrolyzed vegetable protein

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hydrolysis, extraneous polymeric material known as humin, which forms from the interaction of carbohydrate and protein fragments, is generated and subsequently...

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Name of Italy

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linguists and historians. Considerations extraneous to the specifically linguistic reconstruction of the name have formed a rich corpus of solutions that are...

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Attention deficit hyperactivity disorder

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Divergent thinking is the ability to produce creative solutions which differ significantly from each other and consider the issue from multiple perspectives....

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Google Search

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different language Ignoring words – In some search queries containing extraneous or insignificant words, Google search will simply drop those specific...

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Apostrophe

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campaigned for large retailers such as Harrods, Currys, and Selfridges to reinstate their missing punctuation. A spokesperson for Barclays PLC stated, "It...

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Transgender

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never have an extraneous '-ed' tacked onto the end. An '-ed' suffix adds unnecessary length to the word and can cause tense confusion and grammatical errors...

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ABX test

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to X, however, the time delay would be missing if X was really A and present if X was really B. This extraneous cue was removed by inserting a fixed length...

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Black Stone

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millions of touches and kisses it has received. It appeared to me like a lava, containing several small extraneous particles of a whitish and of a yellow substance...

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Alexander Graham Bell

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several particulars from most of the many and varied versions now in circulation, by concluding that extraneous metal was not to blame for failure to locate...

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Cryptic crossword

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crossword has a regular following, and while The Hindu publishes the solutions on the following day, the annotated solution is put up at the website 'The Hindu...

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Microsoft PowerPoint

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larger, higher-quality, and more important graphics and photographs; removing all extraneous decoration, backgrounds, logos and identifications, everything...

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International Phonetic Alphabet

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g. ⟨yᷱ øᪿ⟩) and a combining turned w diacritic ⟨◌ᫀ⟩ for compression (e.g. ⟨uᫀ oᫀ⟩). ⟨◌̫⟩ is the cursive form of ⟨◌ᪿ⟩, and these solutions recall an old...

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Polycoria

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and contract simultaneously with triggers such as light and administered drugs. The extraneous pupil is c. 2.5mm away from the principal pupil. In cases...

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Data and information visualization

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an erroneous conclusion. According to Tufte, chartjunk refers to the extraneous interior decoration of the graphic that does not enhance the message or...

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Frank Lloyd Wright

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of the scene would frequently breach in front of one another, and their lack of extraneous detail, which he called a "gospel of elimination." His interpretation...

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Arthropod

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food see the last entry (on "Wheat Flour") and the definition of "Extraneous material" in Codex Alimentarius, and the standards published by the FDA. Martínez-Muñoz...

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