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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.
^Ron Larson (1 January 2011). Calculus I with Precalculus. Cengage Learning. pp. 4–. ISBN 978-0-8400-6833-0.
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an extraneoussolution (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...
integration.[citation needed] Solutions of differential equations can be implicit or explicit. Extraneousandmissingsolutions Simultaneous equations Equating...
E=\{e^{ix}=1\}} with respect to x ∈ C {\displaystyle x\in \mathbb {C} } is S = 2πZ (see Euler's identity). Equation solving Extraneousandmissingsolutions...
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...
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...
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...
linguists and historians. Considerations extraneous to the specifically linguistic reconstruction of the name have formed a rich corpus of solutions that are...
control and who acts only after carefully weighing all options, the Rational Actor method allows scholars to filter out extraneous details and focus attention...
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...
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...
memory containing the descriptor for the undefined-opcode exception. These extraneous memory accesses turned out to be sufficient for the bus interface to let...
Divergent thinking is the ability to produce creative solutions which differ significantly from each other and consider the issue from multiple perspectives....
hydrolysis, extraneous polymeric material known as humin, which forms from the interaction of carbohydrate and protein fragments, is generated and subsequently...
different language Ignoring words – In some search queries containing extraneous or insignificant words, Google search will simply drop those specific...
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...
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...
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...
campaigned for large retailers such as Harrods, Currys, and Selfridges to reinstate their missing punctuation. A spokesperson for Barclays PLC stated, "It...
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...
still insist that "a square is not a rectangle." (They may introduce extraneous properties to support such beliefs, such as defining a rectangle as a...
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...
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...
larger, higher-quality, and more important graphics and photographs; removing all extraneous decoration, backgrounds, logos and identifications, everything...
an erroneous conclusion. According to Tufte, chartjunk refers to the extraneous interior decoration of the graphic that does not enhance the message or...
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...
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...
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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