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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. .... Only those letters which occur in the [[English alphabet]] are affected; numbers, symbols, whitespace, and all other characters are left unchanged. Because ...

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

...He defined the [[cardinal number|cardinal]] and [[ordinal number|ordinal]] numbers and their arithmetic. Cantor's work is of great philosophical interest, a f ...p. 120 &amp; 143.</ref> on one occasion equating the theory of transfinite numbers with [[pantheism]].<ref name = "daub77102"/> The objections to his work wer ...

However, for physically meaningful numbers of monkeys typing for physically meaningful lengths of time (rather than in ...t eventually succeed "gives a misleading conclusion about very, very large numbers." This is from their textbook on [[thermodynamics]], the field whose statis ...

...e GCD can be expressed as a [[linear combination|sum]] of the two original numbers each multiplied by a positive or negative [[integer]], e.g., {{nowrap begin ...), but the algorithm was generalized in the 19th century to other types of numbers, such as [[Gaussian integer]]s and [[polynomial]]s of one variable. This le ...

...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 ...sales tax administering authority, providing the names and social security numbers of each household member.<ref name="billc3" /> The [[Social Security Admini ...

...t familiar groups is the set of [[integers]] '''Z''' which consists of the numbers === Numbers === ...

...the acceptance of the existence of abstract mathematical entities, such as numbers and sets.<ref name="Ya">{{cite web|author=Yablo, S. | title=A Paradox of Ex ...ostulated in scientific theories, including numbers, should be accepted as real is justified by [[confirmation holism]]. Since theories are not confirmed i ...

...>{{cite news|title=Powderfinger Finds Their Bit Of Happiness|publisher=''[[Real Detroit Weekly]]''|author=McCarthy, Shannon|date=24 May 2001}}</ref> Powder ..., or days".<ref name="popmatters" /> The main critique was for the "faster numbers", stating that "[[Like a Dog]]" "sounds mostly a little bored".<ref name="p ...

...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 ...en experiment and the equipartition theorem was much worse than even these numbers suggest;<ref name="maxwell_1875" >{{cite book | last = Maxwell | first = JC ...

...r]], [[baryon number]], and [[Quark#Flavor quantum numbers|flavour quantum numbers]] are zero.<ref> See p.31 in ...physics)|field]], whereas Maxwell's four equations solve for [[real number|real]] fields. More generally, the normal concept of a Schrödinger [[probability ...

...and discovered its relation to the [[trigonometric function]]s. For any [[real number]] [[φ]], [[Euler's formula]] states that the [[Exponential function# ...and he used analytic methods to gain some understanding of the way [[prime numbers]] are distributed. Euler's work in this area led to the development of the ...

...of processing elements, which flattens out into a constant value for large numbers of processing elements. ...'' are each 64-element vectors of 64-bit [[floating point|floating-point]] numbers."<ref name=PH751>Patterson and Hennessy, p.&nbsp;751.</ref> They are closel ...

...''Gruppentheorie und hyperkomplexe Zahlen'' (Group Theory and Hypercomplex Numbers) ...rich Hecke]]'s ''Theorie der algebraischen Zahlen'' (''Theory of algebraic numbers'', 1908).<ref>{{Harvnb|Dick|1981|pp=80–81}}.</ref> ...

The three numbers ''s''₁, ''s''₂ and ''s''₃ on the [[sides o ...f three possible types: two different [[real number]]s, two identical real numbers (i.e., a degenerate double root), or a pair of [[complex conjugate]] roots. ...

...s usual to limit ''r'' to [[negative and non-negative numbers|non-negative numbers]] ({{nowrap|''r'' ≥ 0}}) and θ to the [[interval (mathematics)|interval]] [ ...se equations will produce a ''k''-petalled rose if ''k'' is [[even and odd numbers|odd]], or a 2''k''-petalled rose if ''k'' is even. If ''k'' is rational but ...

...t aspect of the paradox, "the argument by scale", is a function of the raw numbers involved: there are an estimated 250 billion (2.5 x [[1 E9|10¹¹] ...keptics, such as [[Frank J. Tipler|Frank Tipler]], have put in pessimistic numbers and concluded that the average number of civilizations in a galaxy is much ...

...found that dwarf stars followed a distinct relationship. This allowed the real brightness of a dwarf star to be predicted with reasonable accuracy.<ref na ...re are stars that have a very low abundance of elements with higher atomic numbers than helium—known as [[metal-poor]] stars—that lie just below the main sequ ...

...he inhibitor. Competitive inhibitors are often similar in structure to the real substrate (see examples below). ...ended by [[combinatorial chemistry]] approaches that quickly produce large numbers of novel compounds and [[high-throughput screening]] technology to rapidly ...

[[Image:Semimajorhistogramofkbos.svg|thumb|401 px|Graph showing the numbers of KBOs for a given distance from the Sun. The Plutinos are the "spike" at ...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 ...