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 that this definition is tied to the critical density of the present cosmological era: the critical density changes with cosmological time, but the energy density due to the cosmological constant remains unchanged throughout the history of the universe.

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 that the same set of points would not have, as an accumulation point, any point of the open unit interval ; hence that space cannot be compact.

Note that the non-penalized team has the option to decline any penalty it considers disadvantageous, so a losing team cannot indefinitely prolong a game by repeatedly committing infractions.

Note that any valid SGML or XML document that references an external subset in its DTD, or whose body contains references to parsed external entities declared in its DTD ( including those declared within its internal subset ), may only be partially parsed but cannot be fully validated by validating SGML or XML parsers in their standalone mode ( this means that these validating parsers will not attempt to retrieve these external entities, and their replacement text will not be accessible ).

Although siblinghood is symmetric ( if A is a sibling of B, then B is a sibling of A ) and transitive on any 3 distinct people ( if A is a sibling of B and C is a sibling of B, then A is a sibling of C, provided A is not C ( Note that " is a sibling of " is NOT a transitive relation, since A R B, and B R A implies A R A by transitivity )), it is not reflexive ( A cannot be a sibling of A ).

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 the ICF and ZAAP are essentially identical to CP, but distinguished for software cost control: they are slightly restricted such they cannot be used to run arbitrary operating systems, and thus do not count in software licensing costs ( which are typically based on the number of CPs ).

Note that if n < sub > 1 </ sub > and n < sub > 2 </ sub > are the same, the antisymmetric expression gives zero, which cannot be a state vector as it cannot be normalized.

Note that some metres have an overall rhythmic pattern to the line that cannot easily be described using feet.

Note that, although capitalization can aid in recognizing named entities in languages such as English, this information cannot aid in determining the type of named entity, and in any case is often inaccurate or insufficient.

Note that inferior courts cannot evade binding precedent of superior courts, but a court can depart from its own prior decisions.

( Note that the propagation of the prion depends on the presence of normally folded protein in which the prion can induce misfolding ; animals which do not express the normal form of the prion protein cannot develop nor transmit the disease.

Note that with this construction multiple preorders "" can give the same relation "<", so without more information, such as the equivalence relation, "" cannot be reconstructed from "<".

Note: Christian Scientists, Quakers and the Salvation Army cannot be classified as specifically opposing infant baptism, since they generally do not observe baptism in any form.

Since we've assumed that we can infallibly identify programs for computing squares, we can determine whether t, which depends on a and i, is such a program, and that for every a and i ; thus we have obtained a program that decides whether program a halts on input i. Note that our halting-decision algorithm never executes t, but only passes its description to the squaring-identification program, which by assumption always terminates ; since the construction of the description of t can also be done in a way that always terminates, the halting-decision cannot fail to halt either.

Note: As in all track-and-field events, results cannot count towards records if they are Wind assisted (> 2. 0 m / s ).

Signal processors, such as four-phase modems, cannot change the DSR, but the modulation rate depends on the line modulation scheme, in accordance with Note 4.

**** Note that this axiom precludes the possibility that the consumer cannot decide, and that a consumer is able to make this comparison with respect to every conceivable bundle of goods.

Note that this leaves the fuel at atmospheric pressure, and therefore it cannot travel into a throat which has been pressurized by a supercharger mounted upstream ; in such cases, the entire carburetor must be contained in an airtight pressurized box to operate.

Note the distinction with virtual memory systems ; in this case, the entirety of a process's addressable space must be in core memory, must be contiguous, and its size cannot be larger than the real memory capacity.

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 and can be perpendicular, but cannot be parallel.

Note that a hazard cannot be played unless one's opponent is moving, except for the Speed Limit.

( Note that the conditions under which the cancellation law holds are quite strict, and this explains why Fermat's little theorem demands that p be a prime in order to make a general case for all n. For example, 2 × 2 ≡ 2 × 5 ( mod 6 ), but we cannot conclude that 2 ≡ 5 ( mod 6 ), since 6 is not prime.