However, if no assumptions about initial boundary conditions are made, the fluctuation theorem should apply equally well in reverse, predicting that a system currently in a low-entropy state is more likely to have been at a higher-entropy state in the past, in contradiction with what would usually be seen in a reversed film of a nonequilibrium state going to equilibrium.

However, that particular case is a theorem of Zermelo – Fraenkel set theory without the axiom of choice ( ZF ); it is easily proved by mathematical induction.

However, by Wedderburn's little theorem all finite division rings are commutative and therefore finite fields.

However, the majority are solved via ad hoc methods such as Størmer's theorem or even trial and error.

However, Bell's theorem does not apply to all possible philosophically realist theories.

) However, the fundamental theorem of arithmetic gives no insight into how to obtain an integer's prime factorization ; it only guarantees its existence.

However, even though it cannot be determined whether a particular file is incompressible, a simple theorem about incompressible strings shows that over 99 % of files of any given length cannot be compressed by more than one byte ( including the size of the decompressor ).

However, the one monopoly profit theorem is not true if customers in the monopoly good are stranded or poorly informed, or if the tied good has high fixed costs.

( However, it was subsequently discovered that the theorem breaks down somewhat for stars of non-uniform composition.

However, in certain axiom systems for constructive set theory, the axiom of choice does imply the law of the excluded middle ( in the presence of other axioms ), as shown by the Diaconescu-Goodman-Myhill theorem.

However a result known as the Sonnenschein-Mantel-Debreu theorem suggests that the assumptions that must be made to ensure that the equilibrium is stable and unique are quite restrictive.

However, recent developments attempt to show that if locality is only approximate and the holographic principle is correct, the Weinberg – Witten theorem would not be valid.

However, results such as the fundamental theorem of algebra are simpler when expressed in terms of complex numbers.

However, it is standard practice to assume that the sample mean from a random sample is normal, because of the central-limit theorem.

However, lemmas are sometimes embedded in the proof of a theorem, either with nested proofs, or with their proofs presented after the proof of the theorem.

However, the virial theorem does not depend on the notion of temperature and holds even for systems that are not in thermal equilibrium.

However, the sampling theorem can be extended in a straightforward way to functions of arbitrarily many variables.

However, a measurable function is nearly a continuous function ; see Luzin's theorem.

However, if the random variable has an infinite but countable probability space ( i. e. corresponding to a die with infinite many faces ) the 1965 paper demonstrates that for a dense subset of priors the Bernstein-von Mises theorem is not applicable.

However, it was Pierre-Simon Laplace ( 1749 – 1827 ) who introduced a general version of the theorem and used it to approach problems in celestial mechanics, medical statistics, reliability, and jurisprudence.

However, its importance derives mainly from the multivariate central limit theorem.

However, the choice of dimensionless parameters is not unique: Buckingham's theorem only provides a way of generating sets of dimensionless parameters, and will not choose the most ' physically meaningful '.

However, the choice of dimensionless parameters is not unique: Buckingham's theorem only provides a way of generating sets of dimensionless parameters, and will not choose the most ' physically meaningful '.

However, Fred Richman proved a reformulated version of the theorem that does work .< ref > See Fred Richman ; 1998 ; < cite > The fundamental theorem of algebra: a constructive development without choice </ cite >; available from .</ ref >

However, this assumes that such a mutation is possible.

" However, the DSM is based on an underlying structure that assumes discrete medical disorders that can be separated from each other by symptom patterns.

However, this argument assumes that without disclosure such tools and attacks would not have occurred.

However, about once a week some character spots the fact that HAL is one letter ahead of IBM, and promptly assumes that Stanley and I were taking a crack at the estimable institution ... As it happened, IBM had given us a good deal of help, so we were quite embarrassed by this, and would have changed the name had we spotted the coincidence.

However to demonstrate the concept, this section assumes there is a car accident in a Common Law jurisdiction that does use complicated concepts ...

However, this again assumes that the emergence of life in the entire Universe is rare enough as to limit it to one or few events or origination sites.

However, the BCP process goes beyond risk management's preemptive approach and assumes that the disaster will happen at some point.

However, long-term intensive interactional group psychotherapy assumes diverse and diagnostically heterogeneous group membership, and an open-ended time scale for therapy.

However, this argument assumes that the register values are changed using conventional set and clear operations which inevitably generate entropy.

However, having already received a proposal from him, each assumes in her own way that she has an open invitation to marry Bertie whenever she has a spat with her current fiancé.

However, since he identifies himself as aboard the USS Nimitz, the radio operator assumes it is a hoax — as Admiral Chester W. Nimitz was then on active duty in the U. S. Navy — and the senator's warning is not believed.

However, a modern theoretical treatment by Modinos assumes that the band-structure of the emitting material must also be taken into account.

However, because this formula implicitly assumes the section of the demand curve between those points is linear, the greater the curvature of the actual demand curve is over that range, the worse this approximation of its elasticity will be.

However, classical bargaining theory assumes that each participant in a bargaining process will choose between possible agreements, following the conduct predicted by the rational choice model.

However, this figure does not take into account royal security, nor the money paid by regional councils to fund the costs of visits by members of the Royal Family, and assumes the " official " figure of £ 34m per annum to be divided between every man, woman and child in the land.

However this term is problematic as it lumps together immigrants from the diverse cultures of the United Kingdom, Australia, South Africa, the USA and Canada under one apparently culturally homogeneous umbrella and assumes a common interest based on language and an undefined " Anglo-Saxon " culture.

However, Suetonius is confused in the passage and assumes that Chrestus was alive at the time of the disturbance and was agitating the Jews in Rome.

However, run length limited coding terminology assumes NRZI encoding, so 1 bits indicate changes and 0 bits indicate the absence of change, the above sequence would be expressed as ' 11000101001000001 ', and only runs of zero bits are counted.

However this assumes that concrete knowledge is already present in humans to solve a problem.

However, it is the male who assumes the bulk of care giving and rearing responsibilities ; the female serves only to nurse the infants.

However, it assumes a more personal nature and just as in the West, its form depends on the time of the day and the elapsed time since the last contact with the greeter.

However, this description of Protoavis assumes that Protoavis has been correctly interpreted as a bird.

However, this description of Protoavis assumes that Protoavis has been correctly interpreted as a bird.

However, the manga is fairly obscure, so Majik mistakenly assumes his name refers to the Penaeus monodon, a type of prawn sometimes called " Black Tiger ", resulting in Hartia's receiving the nickname, " Shrimp Man ", much to his own chagrin.