Note that these arguments may indeed have validity, but they require some independent justification of the connection between their terms: otherwise the argument ( as a logical tool ) remains fallacious.

Note that the validity of this alternative within this dilemma does not in any way imply that money can both exist and not exist.

Note that all 4 of these hypothetical Fredkin measuring devices assume some sort of weird notion of absolute space, time, and information that would depend upon the ' alternate-universe engine ' for any empirical validity.

Note that since the validity of fair use depends on the use, and since the tag is deprecated, there should not be any images in this category directly ; all should be in an appropriate subcategory ( typically via the use of a different template ).

printed by Jeffries Bank Note Company, undated and with a 90-day validity clause ; common design of Mercury in circle upper left, all brown & pink:

printed by Jeffries Bank Note Company, dated June 20, no validity clause:

: Senior counsel for the applicant attacked the validity of par 12 of the Practice Note on two grounds.

Note that most of these verses do not distinguish between the conditional election ( Arminian ) and unconditional election ( Calvinist ), but are simply evidence of some type of election.

Note that the conditional expected value is a random variable in its own right, whose value depends on the value of X.

Note that is simply the name of the conditional expectation function.

Note that neither value if true nor value if false expressions can be omitted from the conditional operator without an error report upon parsing.

Note that this is a conditional probability, hence the in the denominator.

Note that the assumption of a joint probability distribution allows us to model uncertainty in predictions ( e. g. from noise in data ) because is not a deterministic function of, but rather a random variable with conditional distribution for a fixed.

Note that in the " historical " tenses ( the imperfect, preterite, and conditional ), a consonant-initial stem undergoes lenition, while a vowel-initial stem is prefixed by d ’.

( Note that in the metalanguage, " everything that is such that X is such that Y " is interpreted as a universal generalization of the material conditional " if anything is such that X then it is such that Y ".

* Note in Columbia Law Review distinguishing conditional preemption vs. commandeering

#* Note: This fact provides a proof of the infinitude of primes distinct from Euclid's Theorem: if there were finitely many primes, with p being the largest, we reach an immediate contradiction since all primes dividing 2 < sup > p </ sup > − 1 must be larger than p .</ li >

Note that one formulation of AC is that the Cartesian product of a family of nonempty sets is nonempty ; but since the empty set is most certainly compact, the proof cannot proceed along such straightforward lines.

Note that in the United States the term " degrees proof " is not used.

( Note that it takes values into R, rather than C ; this is for physical reasons, and doesn't really matter for this proof.

Note that with both copy holding and double reading, responsibility for a given proof is necessarily shared by two individuals.

Note that this proof of existence of stellar black holes is not entirely observational but relies on theory: We can think of no other object for these massive compact systems in stellar binaries besides a black hole.

Note that the foregoing proof of analyticity derived an expression for a system of n different function elements f < sub > i </ sub >( x ), provided that x is not a critical point of p ( x, y ).

Note that the anticommutation relations for the Pauli matrices make the proof of the above defining property trivial.

Note that the proof is clearly only valid for simple cyclic quadrilaterals ; if the quadrilateral is complex then K will be located outside the line segment AC, so AK − CK =± AC, giving the expected result.

Note that though the ideal gas itself contains no additional energy, the compressed gas does exert an increased pressure.

Note that chemists often write H < sup >+</ sup >( aq ) and refer to the hydrogen ion when describing acid-base reactions but the free hydrogen nucleus, a proton, does not exist alone in water, it exists as the hydronium ion, H < sub > 3 </ sub > O < sup >+</ sup >.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

* Note: Botswana does not have a westernmost point as the western section is formed by the 22nd meridian of longitude east of Greenwich.

Note that the associative property does not hold for expressions that include non-linear operators, such as the antilinear time reversal operator in physics.

Note that traditional Berkeley DB also supports a Java API, but it does so via JNI and thus requires an installed native library.

* Note: technically Chad does not have an easternmost point, the northern section of the border being formed by the 24 ° of latitude

Note: in Greek, the term for " consul " is " ypatos ", which translates as " supreme one ", and hence does not necessarily imply a joint office.

Note that in many cases, digital cable telephone service is separate from cable modem service being offered by many cable companies and does not rely on Internet Protocol ( IP ) traffic or the Internet.

Note that this does not require 100 % awareness from the onset of the data warehousing effort, no master plan is required upfront.

Note that a dominatrix does not necessarily dominate a male partner ; a dominatrix may well have female submissives, nor must the role of a dominatrix involve pain toward the submissive ; her domination can be verbal, involving humiliating tasks and servitude.

( Note that anti-trust regulation does take into account cases when only large companies are viable because of the nature of an industry, but favors many participants over few, whenever possible.

Note that materialism does not necessarily imply egoism, as indicated by Karl Marx, and the many other materialists who espoused forms of collectivism.

( Note, chart does not include population statistics.

Note that this derivation does assume that ƒ ( x ) is sufficiently differentiable and well-behaved ; specifically, that ƒ may be approximated by polynomials ; equivalently, that ƒ is a real analytic function of exponential type.

Note that Reynolds does not object to the Marxist use of the term feudalism.

* * Note: Guinea does not have a northern-most point, this section of the border being formed by a straight horizontal line

* * Note: Guinea-Bissau does not have a northern-most point, the border here being formed by a straight horizontal line

Note that chair does not change form between " the chair is here " ( subject ) and " I saw the chair " ( direct object ), a distinction made by word order and context.

Note that ƒ cannot be extended to a homomorphism of rings ( from the complex numbers to the real numbers ), since it does not preserve addition:

Note that this " high temperature " approximation does not distinguish between fermions and bosons.

* * Note: Morocco does not have a southern-most point, the border being formed by a straight horizontal line

Note: In cases where the optical design of a microscope produces an appreciable lateral separation of the two beams we have the case of classical interference microscopy, which does not result in relief images, but can nevertheless be used for the quantitative determination of mass-thicknesses of microscopic objects.

( Note that while Mercury does allow impure functionality, it is not necessary in most software, and serves primarily as a way of calling foreign language code.