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...me action can be used for encoding and decoding. The algorithm provides no real [[cryptography|cryptographic]] security and should never be used for such. ...tandard|DES]] is little better than ROT13 these days." Also, in a play on real terms like "double DES", the terms "double ROT13", "ROT26" or "2ROT13" crop ...

...[[mathematical rigour]], taking into account preferred development of the real numbers, background assumptions, historical context, and target audience. ...so occur in a classic investigation of the infinitude of the entire set of real numbers. ...

...set|infinite]] and [[well-order|well-ordered sets]], and proved that the [[real number]]s are "more numerous" than the [[natural number]]s. In fact, [[Cant ...itional areas of mathematics (such as [[algebra]], [[Mathematical analysis|analysis]] and [[topology]]) in a single theory, and provides a standard set of axio ...

...al algorithm was described only for natural numbers and geometric lengths (real numbers), but the algorithm was generalized in the 19th century to other ty ...ructing [[continued fraction]]s, in the [[Sturm chain]] method for finding real roots of a polynomial, and in several modern [[integer factorization]] algo ...

...s would be subject to the FairTax, as would renting apartments and other [[real property]].<ref name="money"/> In comparison, the current tax system also t ...[[FactCheck]] called the presentation misleading, saying that it hides the real truth of the tax rate.<ref name="FactCheck">[[#refMiller2007|Miller, 2007]] ...

...mathematics]] greatly simplify the study of [[geometry|geometrical]] or [[analysis|analytical objects]]. A group is said to [[group action|act]] on another ma ...theory enables simplification of [[quantum mechanics|quantum mechanical]] analysis of these properties.<ref> {{Harvard citations|nb = yes|last1 = Conway|last2 ...

...ical positions as to those of others, subjecting each position to rigorous analysis until he exposes its flaws.<ref name=King170>[[Peter J. King|King, P.J.]] ' ...ostulated in scientific theories, including numbers, should be accepted as real is justified by [[confirmation holism]]. Since theories are not confirmed i ...

...r [[mass number]]s. These probability density functions have [[dimensional analysis|dimensions]] of probability times inverse speed; since probability is dimen ...reedom ''x'' contributes only a multiple of ''x^s'' (for a fixed real number ''s'') to the energy, then in thermal equilibrium the average energy ...

...physics)|field]], whereas Maxwell's four equations solve for [[real number|real]] fields. More generally, the normal concept of a Schrödinger [[probability ...which photons "clone" themselves) was predicted by Einstein in his kinetic analysis, and led to the development of the [[laser]]. Einstein's derivation inspire ...

...ern mathematical terminology and notation, particularly for [[mathematical analysis]], such as the notion of a [[function (mathematics)|mathematical function]] ===Analysis=== ...

...ents. Bernstein's conditions<ref>Bernstein, A. J. (October 1966). "Program Analysis for Parallel Processing,' IEEE Trans. on Electronic Computers". EC-15, pp.& * [[Unstructured grid]] problems (such as found in [[finite element analysis]]) ...

...dition=2nd}}</ref><ref>{{cite book|author=Needham, T|title="Visual Complex Analysis"|isbn=978-0-19-853446-4|publisher=Oxford University Press|location=New York ...be of three possible types: two different [[real number]]s, two identical real numbers (i.e., a degenerate double root), or a pair of [[complex conjugate] ...

...tle = Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis| publisher = McDougal Littell| location = Evanston, Illinois| isbn = 0-395- ...(in radians, [0,&nbsp;2π) or (−π,&nbsp;π]).<ref>{{cite book|title=Complex Analysis (the Hitchhiker's Guide to the Plane)|first=Ian|last=Stewart|coauthors=Davi ...

...such searches are being carried out at great distances and rely on careful analysis of very subtle evidence. This limits possible discoveries to civilizations ...ce SHGb02 plus 14a|Radio source SHGb02+14a]] was isolated by [[SETI@home]] analysis, although it has largely been discounted by further study. There are numer ...

...he inhibitor. Competitive inhibitors are often similar in structure to the real substrate (see examples below). ...second binding site.<ref>*Irwin H. Segel, ''Enzyme Kinetics : Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems''. Wiley–Interscience; ...

...ublications/showman-malhotra-1999.pdf|format=pdf|pmid=10506564}}</ref> The analysis of high-resolution, [[near-infrared]] and [[UV]] [[spectrum|spectra]] obtai ...edu/~espoclass/homework/5830_2008_homework/Ch17.pdf|format=pdf}}</ref> The real breakthrough happened later with the ''[[Voyager 1]]'' and ''[[Voyager 2|2] ...

...rapid decline in objects of 100&nbsp;km or more in radius beyond 50 AU is real, and not due to observational bias. Possible explanations include that mate ...pacts or outgassing.<ref name=KBOKBO /> However, Jewitt and Luu's spectral analysis of the known Kuiper belt objects in 2001 found that the variation in colour ...

:with [[real number]]s ''a'' and ''b''. This is an early example of a [[Curve|mechanical ...''Stomachion'' was also discovered in the palimpsest, with a more complete analysis of the puzzle than had been found in previous texts. The palimpsest is now ...

...s as a result of major advances in [[telescope]] technology as well as the analysis of copious data from satellites such as [[COBE]],<ref name=cobe> ...es Lemaître]] in 1927,<ref name=gl1927 /> well before Hubble made his 1929 analysis and observations, and it remains the cornerstone of the Big Bang theory as ...

...and have only to investigate their amount by observation. But light is no real property of mass. The existence of numberless visible stars can prove noth Since this analysis uses the non-relativistic formula ''p''²/2''m'' for the kinetic ...