Note that this definition cannot be expressed in the language of set theory itself.

Note that with this definition, two elements a and b may very well have several greatest common divisors, or none at all.

Note: The above definition of group velocity is only useful for wavepackets, which is a pulse that is localized in both real space and frequency space.

Note however that Kierkegaard's meaning of " nihilism " differs from the modern definition in the sense that, for Kierkegaard, levelling led to a life lacking meaning, purpose or value, whereas the modern interpretation of nihilism posits that there was never any meaning, purpose or value to begin with.

Note that the example net given above on the neighborhood system of a point x does indeed converge to x according to this definition.

Note that an alternate definition of preorder requires the relation to be irreflexive.

Note that < em > finite </ em > in this definition is essential.

Note that the tensor rank of a matrix can also mean the minimum number of simple tensors necessary to express the matrix as a linear combination, and that this definition does agree with matrix rank as here discussed.

Note, however, that this definition is not universal.

Note: if as in the simplified definition, then is automatically 1, and the order of modulo is automatically.

Note that the definition is somewhat ambiguous because the user of a program can be another program and, if the latter is a portion of the set of program that is required to be interoperable, it might well be that it does need to have knowledge of the characteristics of other units.

Note that when this definition is used, the connection between the NA and the acceptance angle of the fiber becomes only an approximation.

Note that with this definition, unlike SNR, a SINAD reading can never be less than 1 ( i. e. it is always positive when quoted in dB ).

Note that some references may use the reciprocal as the definition.

Note that the enriched structure on hom-sets is a consequence of the three axioms of the first definition.

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

Note that the definition of PSPACE-completeness is based on asymptotic complexity: the time it takes to solve a problem of size n, in the limit as n grows without bound.

Then x is an interior point of S if there exists a neighbourhood of x which is contained in S. Note that this definition does not depend upon whether neighbourhoods are required to be open.

Note that by definition, a linear combination involves only finitely many vectors ( except as described in Generalizations below ).

Note that whereas the Reynolds number and Grashof number are subscripted with a length scale variable, the Prandtl number contains no such length scale in its definition and is dependent only on the fluid and the fluid state.

Note that this definition of V depends on the gauge choice for the vector potential A ( the gradient of any scalar field can be added to A without changing B ).

Note that this definition is very different from that given by Weberling.

" Note that in a cryptic clue, there is almost always only one answer that fits both the definition and the wordplay, so that when you see the answer, you know it is the right answer-although it can sometimes be a challenge to figure out why it is the right answer.

In radar applications, it ranges from 12-18 GHz according to the formal definition of radar frequency band nomenclature in IEEE Standard 521-2002 .< ref > Note that in the band 11. 2 – 12 GHz the working definitions of K < sub > u </ sub > band and X band overlap ; satellite communications engineers would generally regard frequencies above 11. 2 GHz as being part of the K < sub > u </ sub > band .</ ref >

( Note: So far as State Police cars are concerned, only their replacement is under this division ).

Note, however, that it is six inches shorter at the forward end.

Note another piece of wood six inches wide is fastened to the transom between these pieces.

Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.

Note that the mass threshold is four times that of 1958 Alpha and that the flux is one fifth as large.

Note that the mass scale is one to two orders of magnitude greater than some previously used ; ;

Note also that if Af, then Af is divisible by the polynomial p, because Af contains each Af as a factor.

Note that flexural strength is not always improved by simply increasing the density, nor is the change always proportional from one formulation to another.

Most European domestic power supplies run at 230 V, so the current drawn by a particular European appliance ( in Europe ) will be less than for an equivalent American one ( in the United States ).< ref group =" Note "> The formula for power is given by

Note that this premise uses the phrase " is not ", a form of " to be "; this and many other examples show that he did not intend to abandon " to be " as such.

Note: This list is limited to linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's Einführung in 1952.

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 that there is no directly corresponding concept in the German language.

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 that the above formula is only applicable to classical ideal gases and not Bose – Einstein or Fermi gases.

Note that this pressure increase is more than a simple 10: 1 compression ratio would indicate ; this is because the gas is not only compressed, but the work done to compress the gas has also heated the gas and the hotter gas will have a greater pressure even if the volume had not changed.

Note that this is not the same as a monophyly in which all descendants of a common ancestor are included.

Note: because Solar System bodies are never perfect diffuse reflectors, astronomers use empirically derived relationships to predict apparent magnitudes when accuracy is required.

Note that this is subtly different to the ' thanks ' list in the original BBC Model B.