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Page "Axiom of choice" ¶ 41
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Assuming and ZF
Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model ( the constructible universe ) which satisfies ZFC and thus showing that ZFC is consistent.

Assuming and is
Assuming the lower figure for the big blast and one shot estimated by the Japanese at 10 megatons, a conservative computation is that the 24 announced tests produced a total yield of at least 60 megatons.
Assuming the weather is halfway decent that day, hundreds of thousands of persons will mass along this thoroughfare as President John F. Kennedy and retiring President Dwight D. Eisenhower leave Capitol Hill following the oath-taking ceremonies and ride down this historic ceremonial route.
Assuming that the pixel color is expressed using straight ( non-premultiplied ) RGBA tuples, a pixel value of ( 0. 0, 0. 5, 0. 0, 0. 5 ) implies a pixel which has 50 % of the maximum green intensity and 50 % opacity.
Assuming that the ion is accelerated during a very short interval, the ion can be assumed to be travelling at constant velocity.
Assuming that 10 – 15 % of bread is thrown away as stale, if it could be made to stay fresh another 5 – 7 days then perhaps 2 million tons of flour per year would be saved.
Assuming average population densities of 0. 25 animals per km² in regions where it is known to be common or abundant, and 0. 02 per km² elsewhere, and with a total area of occupancy of 327, 000 km², a total population estimate of approximately 28, 000 is suggested.
Assuming a fixed sample size, the technique gives more accurate results when most of the variation in the population is within the groups, not between them.
:< u > The Copenhagen Interpretation </ u >: Assuming wave functions are not real, wave-function collapse is interpreted subjectively.
Assuming the Axiom of choice, is regular for each α.
Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.
Assuming that the strength of the cable is proportional to its density per unit length, the weight, w, per unit length of the chain can be written T / c, where c is constant, and the analysis for nonuniform chains can be applied.
Assuming that the rule is known, one can derive the function that is used above in the classical heat calculation with respect to pressure.
Assuming that translation is not used transformations can be combined by simply multiplying the associated transformation matrices.
Assuming we can define at least one nonreal complex number, however, a complex number is definable if and only if both its real part and its imaginary part are definable.
Assuming that the visible material makes up only a small part of the cluster is the most straightforward way of accounting for this.

Assuming and consistent
Assuming Chavez was approximately 10 years old in 1979, that places the events of Debt of Honor to be in or near 2000, although the overall technology presented in the novel and its successive novels Executive Orders and Rainbow Six ( especially in regards to the sophistication of internet technology ) are more consistent with the mid-1990's.
Assuming that the routing tables are consistent, the simple algorithm of relaying packets to their destination's next hop thus suffices to deliver data anywhere in a network.
Assuming the validity of Bell's theorem, any deterministic hidden-variable theory which is consistent with quantum mechanics would have to be non-local, maintaining the existence of instantaneous or faster-than-light relations ( correlations ) between physically separated entities.
Assuming you catch the balls at a consistent level, then the timing of when the balls land is already determined.

Assuming and Paul
Assuming they slept together, Paul rushes Becky out of his apartment and hopes never to see her again.

Assuming and Cohen
Assuming that the United States is the most significant destination of immigration for Israelis, the sociologist Yinon Cohen estimated that in 2000 the total number of the Israeli Jews who live outside Israel was between 300, 000 and 350, 000.

Assuming and employed
Assuming increased acceptance, the milling industry will have to adapt to triticale, as the milling techniques employed for wheat are unsuited to triticale.

Assuming and developed
Assuming the movement to be small, the image constraint at with Taylor series can be developed to get:

Assuming and for
Assuming no loss of time when moving a car from one station to another, the longest stage on the assembly line determines the throughput ( 20 minutes for the engine installation ) so a car can be produced every 20 minutes, once the first car taking 35 minutes has been produced.
Expansion of U. S. copyright law ( Assuming authors create their works at age 35 and live for seventy years )
Assuming that an interaction will occur ( with 100 % probability ) if the projectile hits the solid, and not at all ( 0 % probability ) if it misses, the total interaction probability for the single projectile will be the ratio of the area of the section of the solid ( the cross section, represented by ) to the total targeted area.
Assuming the stones were used for chiefly houses, it can be argued that Chamorro society was becoming more stratified, either from population growth or the arrival of new people.
Assuming otherwise as is done above will lead to lower GWPs for other gases than a more detailed approach would.
Assuming leadership of the Indian National Congress in 1921, Gandhi led nationwide campaigns for easing poverty, expanding women's rights, building religious and ethnic amity, ending untouchability, increasing economic self-reliance, and above all for achieving Swaraj — the independence of India from British domination.
Assuming the data is reliable, reasons for falling growth rates and fertility rates probably include late marriage, urbanization, limited housing space, and the expectation that women would participate equally in terms of work hours in the labor force.
For instance, raising the note B to B is equal to the note C. Assuming all such equivalences, the complete chromatic scale adds five additional pitch classes to the original seven lettered notes for a total of 12 ( the 13th note completing the octave ), each separated by a half-step.
Assuming both sidebands are symmetric, which is the case for a normal AM signal, no information is lost in the process.
Statistical hypothesis tests answer the question Assuming that the null hypothesis is true, what is the probability of observing a value for the test statistic that is at least as extreme as the value that was actually observed ?.
Assuming the liquid is an ideal solution, and using the formula for the chemical potential of a gas, gives:
Assuming that it is possible to distinguish an observation corresponding to one of the discrete probability masses from one which corresponds to the density component, the likelihood function for an observation from the continuous component can be dealt with as above by setting the interval length short enough to exclude any of the discrete masses.
Assuming that decision-makers make cost-benefit analyses when deciding to use force, China's doctrine calls for acquiring a nuclear arsenal only large enough to destroy an adversary ’ s " strategic points " in such a way that the expected costs of a first strike outweigh the anticipated benefits.
Assuming that for the particle's actual velocity, we have that.
Assuming that the vice president of the Executive Yuan would be third in line for the presidency, the current line of succession is:
Assuming that in the context cheese means some type of dairy product, the Euler diagram has the cheese zone entirely contained within the dairy-product zone — there is no zone for ( non-existent ) non-dairy cheese.
Assuming that the ion and electron saturation current is the same for each probe, then the formulas for current to each of the probe tips take the form

1.043 seconds.