It is also consistent with ZF + DC that every set of reals is Lebesgue measurable ; however, this consistency result, due to Robert M. Solovay, cannot be proved in ZFC itself, but requires a mild large cardinal assumption ( the existence of an inaccessible cardinal ).

Reduced to its simplest terms, it is an assumption of a collective duty to compensate for the inability of individuals to cope with the rigors of the era.

The implicit assumption of this response is that history is reversible.

The basic truth in the reactionary response is to be found in its realistic assumption of the primacy of the real over the ideational.

But this truth is distorted by its extreme application: the assumption of the separate existence of tradition.

Here we may observe that at least one modern philosophy of history is built on the assumption that ideas are the primary objectives of the historian's research.

Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.

The defect of these proposals is in their attempt to outrun history and their assumption that because something may be desirable it is also possible.

The threshold mass is derived from the momentum threshold with the assumption of a mean impact velocity of Af in the U.S. work and Af in the U.S.S.R. work.

The mass scale used in Table 5-1 was derived on the assumption that the motion of the glowing trail is related to the momentum transfer to the trail by the meteorite, permitting the calculation of the mass if the velocity is known ( Cook and Whipple, 1958 ).

If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

This contradicts the preceding observations, and so, under the assumption of this paper, we must reject the possibility that **zg is a Af curve on a quadric surface.

The existence of conflict and of vigorous union demand for an increase in money wages does not contradict the assumption that the union is willing to settle for cost-of-living and productivity-share increases as distinct from a cost-raising increase in the basic wage rate.

The underlying assumption, of course, is that only sight and touch enable us, in any precise and fully dependable way, to locate objects in space beyond us, the other senses being decidedly inferior, if not totally inadequate, in this regard.

This is an assumption with which few would be disposed to quarrel.

-- On the basis of a differentiability assumption in function space, it is possible to prove that, for materials having the property that the stress is given by a functional of the history of the deformation gradients, the classical theory of infinitesimal viscoelasticity is valid when the deformation has been infinitesimal for all times in the past.

This conclusion is dependent on the assumption that traditional sex mores will continue to sanction both premarital chastity as the `` ideal '', and the double standard holding females primarily responsible for preserving the ideal.

What I find appalling -- and really dangerous -- is the American assumption that the Negro is so contented with his lot here that only the cynical agents of a foreign power can rouse him to protest.

This has largely replaced adaptive expectations in macroeconomic theory since its assumption of optimality of expectations is consistent with economic theory.

So, under the assumption that the theory is consistent, there is no such number.

However, the Novikov self-consistency principle is intended to go beyond just the statement that history must be consistent, making the additional nontrivial assumption that the universe obeys the same local laws of physics in situations involving time travel that it does in regions of spacetime that lack closed timelike curves.

Hilbert aimed to show the consistency of mathematical systems from the assumption that the " finitary arithmetic " ( a subsystem of the usual arithmetic of the positive integers, chosen to be philosophically uncontroversial ) was consistent.

So, under the assumption that the theory is consistent, there is no such number.

Gödel's original statement and proof of the incompleteness theorem requires the assumption that the theory is not just consistent but ω-consistent.

These restrictions are consistent with the grounded belief ( or assumption ) that causal influences cannot travel faster than the speed of light and / or backwards in time.

More precisely, it shows that the mere assumption of the existence of the set of natural numbers as a totality ( an actual infinity ) suffices to imply the existence of a model ( a world of objects ) of any consistent theory.

Others, such as replicated objects and live distributed objects, are more non-standard, in that they abandon the assumption that an object resides in a single location at a time, and apply the concept to groups of entities ( replicas ) that might span across multiple locations, might have only weakly consistent state, and whose membership might dynamically change.

Even Thiele's assumption that the years of captivity were measured from Nisan does not reconcile Ezekiel's chronology for the captivity of Jeconiah with a 586 date, and the calculation given above that uses the customary Tishri-based years yields the summer of 587, consistent with all other texts in Ezekiel related to Jeconiah's captivity.

TIQM is explicitly non-local and, as a consequence, logically consistent with Counterfactual definiteness ( CFD ), the minimum realist assumption.

All studies are consistent with the assumption that promoter escape reduces the lifetime of the sigma-core interaction from very long at initiation ( too long to be measured in a typical biochemical experiment ) to a shorter, measurable lifetime upon transition to elongation.

Some conceptual ambiguity persists, but each conceptualization has in common the general underlying assumption that emotional labor involves managing emotions so that they are consistent with organizational or occupational display rules, regardless of whether they are discrepant with internal feelings.

He argues that " in GAAP ... material facts be disclosed in a conservative, consistent, and reliable manner ", and that " Financial statements be prepared under the assumption that the users of such financial statements are reasonably intelligent, reasonably diligent, and are people who understand not only the uses, but also the limitations, of GAAP ... he most GAAP can give ... are objective benchmarks which the analyst then uses as a tool to determine his, or her, version of economic truth and economic reality.

Under certain engineering assumptions ( e. g. besides the above assumptions for a constant failure rate, the assumption that the considered system has no relevant redundancies ), the failure rate for a complex system is simply the sum of the individual failure rates of its components, as long as the units are consistent, e. g. failures per million hours.

It involves the assumption that fertilization in humans typically occurs a consistent period ( 14 days ) from the onset of the LMP.

In physics as in all of science, contradictions and paradoxes are generally assumed to be artifacts of error and incompleteness because reality is assumed to be completely consistent, although this is itself a philosophical assumption.

Though the paper did not provide any explanation for why amino acid differences in a protein should accumulate at a uniform rate ( the essential assumption of the molecular clock ), it did show that the results were fairly consistent with those of paleontologists.

An additional problem discovered in mathematical modelling is that the assumption of the identity of total production prices and total values ( or the identity of total surplus value and total profits ) cannot be maintained simultaneously with the assumption that the rate of profit on production capital is the same for all industries-to create a consistent theory requires making additional assumptions.

The coherency principle in Bayesian decision theory is the assumption that personal probabilities follow the ordinary rules for probability calculations ( where the validity of these rules corresponds to the self-consistency just referred to ) and thus that consistent decisions can be obtained from these probabilities.

This is how he was defined by scholars for most of history, and Graves uses these peculiarities to develop a sympathetic character whose survival in a murderous dynasty depends upon his family's incorrect assumption that he is a harmless idiot.

Exercise as a teaching tool is deliberately omitted because of a common mistaken assumption that there exists a " correct " position.

The latter is the difference quotient for g at a, and because g is differentiable at a by assumption, its limit as x tends to a exists and equals g ′( a ).

Furthermore, because f is differentiable at g ( a ) by assumption, Q is continuous at g ( a ).

In this case, the smart bet is " heads " because the empirical evidence — 21 " heads " in a row — suggests that the coin is likely to be biased toward " heads ", contradicting the general assumption that the coin is fair.

Robert A. Heinlein originally coined the term grok in his 1961 novel Stranger in a Strange Land as a Martian word that could not be defined in Earthling terms, but can be associated with various literal meanings such as " water ", " to drink ", " life ", or " to live ", and had a much more profound figurative meaning that is hard for terrestrial culture to understand because of its assumption of a singular reality.

These systems faced initial skepticism, based on the assumption that applications do not have significant parallelism, because of Amdahl's law, but the success of early systems such as nCUBE and the fast progress in microprocessor performance following Moore's law led to a fast replacement.

In many real-life transactions, the assumption fails because some individual buyers or sellers have the ability to influence prices.

This was an enormous theoretical leap, but the concept was strongly resisted at first because it contradicted the wave theory of light that followed naturally from James Clerk Maxwell's equations for electromagnetic behavior, and more generally, the assumption of infinite divisibility of energy in physical systems.

# exact or approximate normality of observations: The assumption of normality is often erroneous, because many populations are not normal.

In the classical account strictly and purely in terms of cyclic processes, the spatial interior of the ' working body ' of a cyclic process is not considered ; the ' working body ' thus does not have a defined internal thermodynamic state of its own because no assumption is made that it should be in thermodynamic equilibrium ; only its inputs and outputs of energy as heat and work are considered.

Wilson's wife Edith strongly disliked Marshall because of what she called his " uncouthed " disposition, and also opposed his assumption of the presidency.

Given these assumptions, the constraint that time travel must not lead to inconsistent outcomes could be seen merely as a tautology, a self-evident truth that cannot possibly be false, because if you make the assumption that it is false this would lead to a logical paradox.

The original VeriSign implementation broke this assumption for mail, because it would always resolve an erroneous domain name to that of SiteFinder.

In May 2011, a case was reported in the United Kingdom in which a 15-month-old child who turned out to have Neurofibromatosis type I was misdiagnosed as being abused under the assumption that the mother had Münchausen syndrome by proxy, because the child gained weight while in hospital and lost weight while at home.

We can use this consensus as a pragmatic guide, either on the assumption that it seems to approximate some kind of valid reality, or simply because it is more " practical " than perceived alternatives.

" Through media advertisements, production and distribution of literature, producing music and organizing person-to-person evangelism, the organization asserts that " a specifically Jewish mission " is necessary, saying, " Jewish people tend to dismiss evangelistic methods and materials that are couched in Christian lingo, because they reinforce the assumption that Jesus is for ' them ' not ' us '.

Hamilton's later clarifications often go unnoticed, and because of the persistence of the long standing assumption that kin selection theory necessarily predicts that social cooperation requires innate powers of kin recognition, some theorists have tried to clarify the position in recent work:

He questioned the underlying assumption that the Masoretic text must be more authentic simply because it has been more widely accepted as the authoritative Hebrew version of the Pentateuch:

The concept of bounded rationality revises this assumption to account for the fact that perfectly rational decisions are often not feasible in practice because of the finite computational resources available for making them.

A further assumption is necessary, because chess performance in the above sense is still not measurable.

These fragments disappointed Romantic scholars as not matching the writer's great reputation, partly because Fronto's teachings, with their emphasis on studying ancient writers in search of striking words, were not in accordance with current fashion ( Italy, where not only Mai but Leopardi enthused over them, was an exception ), partly because they gave no support to the assumption that Fronto had been a wise counsellor to Marcus Aurelius ( indeed, they contain no trace of political advice ), partly because his frequent complaints about ill-health, especially those collected in book 5 of Ad M. Caesarem, aroused more annoyance than compassion ; these adverse judgements were reversed once Fronto was read for what he was rather than what he was not, as already in the sympathetic treatment by Dorothy Brock, Studies in Fronto and his Age ( Cambridge: Cambridge University Press, 1911 ).