Note that any model of ZF ¬ C is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true.

Note, however, that the fifth article did not completely deny perseverance of the saints ; Arminius, himself, said that " I never taught that a true believer can … fall away from the faith … yet I will not conceal, that there are passages of Scripture which seem to me to wear this aspect ; and those answers to them which I have been permitted to see, are not of such as kind as to approve themselves on all points to my understanding.

Note that although the carbonate salts of most metals are insoluble in water, the same is not true of the bicarbonate salts.

Note that the validity of a conditional proof does not require that the CPA is actually true, only that if it is true it leads to the consequent.

Note that the previous expression holds true only if the kinetic energy flow rate is conserved between system inlet and outlet.

Note that this statement is only true when the refractive indices of both materials are real numbers, as is the case for materials like air and glass.

Note, this is not true of the extension of propositional logic to other logics like first-order logic.

( Note that these relations are true for theoretical and experimental values, but not between experimental and theoretical values.

Note that stress is not a true pressure since it is not scalar.

Note that reporting the beliefs of others in a non-fiction format is not necessarily an endorsement of the ultimate veracity of those beliefs, it is simply saying it is true that people believe them ( for such topics as mythology, religion ).

Note, however, that the converse is not true in general, i. e. zero skewness does not imply that the mean is equal to the median.

Note that this is also true if the boundary is the empty set, e. g. in the metric space of rational numbers, for the set of numbers of which the square is less than 2.

Note that the above considerations are strictly speaking true for the geometric horizon only: the horizon as it would appear for an observer at sea level on a perfectly smooth Earth without an atmosphere.

Note that the Bernstein-von Mises theorem asserts here the asymptotic convergence to the " true " distribution because the probability space corresponding to the discrete set of events is finite ( see above section on asymptotic behaviour of the posterior ).

Note that a true isotropic radiator does not exist in practice.

Note that the visible part of the monocot plant ( left ) is actually the first true leaf produced from the meristem ; the cotyledon itself remains within the seed

Note that both of these are probabilities in a measure theoretic sense, and neither of these is the true probability of expiring in-the-money under the real probability measure.

Note that for this statement to be true, k must be a constant, or else the k can't be taken outside the limit in the line marked (*).

Note that the frequency of this condition does not indicate the true prevalence of chimerism.

** Note: In the early years of the Junior tournament, Canada did not send a true National Junior team to the event.

( Note that running time is measured in terms of the size of the input, which in this case is ~ log n, that being the number of bits needed to represent the number n .) The elliptic curve primality test can be proven to run in O (( log n )< sup > 6 </ sup >), but only if some still unproven ( but widely assumed to be true ) statements of analytic number theory are used.

Note, however, that these are generalizations, and some of these may not be true for specific dialects:

Note that the last phrase is not required to be said if the speaker has a personal or moral objection, as is true of all oaths administered by the United States government ; Article Six of the United States Constitution requires that there be no religious test for public office.

Note that this is only an approximation that holds true when the orbiting body is of considerably lesser mass than the central one, and eccentricity is close to zero.

Note that the two-sample test checks whether the two data samples come from the same distribution.

Note that not every probability distribution has a defined mean ; see the Cauchy distribution for an example.

( Note that for a discrete distribution the sample skewness may be undefined ( 0 / 0 ), so its expected value will be undefined.

Note that personal ( per capita ) income distribution, given in this table, is not exactly comparable with household income distribution, given in the previous table, because poor households tend to have more members.

Note that the terms indicate the origin of the groups, not their modern distribution: the water deer, for example, is a New World species but is found only in China and Korea.

Note that under either hypothesis, the distribution of the data is fully specified ; there are no unknown parameters to estimate.

Note that this definition of the negative binomial distribution does not easily generalize to a positive, real parameter r.

Note that the obvious compatibility condition, namely, that this marginal probability distribution be in the same class as the one derived from the full-blown stochastic process, is not a requirement.

Note that both types of predictive distributions have the form of a compound probability distribution ( as does the marginal likelihood ).

Note how the equation above reduces to that of the univariate normal distribution if is a matrix ( i. e. a real number ).

Note that knowing that alters the variance, though the new variance does not depend on the specific value of a ; perhaps more surprisingly, the mean is shifted by ; compare this with the situation of not knowing the value of a, in which case x < sub > 1 </ sub > would have distribution

Note that the acceptance ratio indicates how probable the new proposed sample is with respect to the current sample, according to the distribution.

Note that the t-distribution ( red line ) becomes closer to the normal distribution as increases.

( Note that the Cauchy distribution and this spectrum differ by scale factors.

Note that the examples are sometimes said to demonstrate that the Pearson correlation assumes that the data follow a normal distribution, but this is not correct.

Note that although we are looking at success / failure, the data are not accurately modeled by the binomial distribution, because the probability of success on each trial is not the same, as the size of the remaining population changes as we remove each marble.

( Note that this particular case of the Bernoulli distribution has the lowest possible excess kurtosis ; this can be proved by Jensen's inequality as follows.

Note that the higher the polytropic index, the more condensed at the centre is the density distribution.

Note that although this model is termed a " Gaussian chain ", the distribution function is not a gaussian ( normal ) distribution.

Note that a " stationary process " is not the same thing as a " process with a stationary distribution ".

Note also that the function A ( θ ) or equivalently g ( θ ) is automatically determined once the other functions have been chosen, and assumes a form that causes the distribution to be normalized ( sum or integrate to one over the entire domain ).