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 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 the intersection of the two circles — the distinction between short a, i and u is made by both speakers, but Arabic lacks the mid articulation of short vowels, while Hebrew lacks the distinction of vowel length.

Note that using a hierarchical system like this ( assuming it is done carefully ) changes the intersection computational time from a linear dependence on the number of objects to something between linear and a logarithmic dependence.

: Note: For ease of understanding, this discussion uses the terms intersection, road and map — however, formally these terms are vertex, edge and graph, respectively.

Note that there is no corresponding axiom of intersection.

Note that these properties are also satisfied if " interior ", " subset ", " union ", " contained in ", " largest " and " open " are replaced by " closure ", " superset ", " intersection ", " which contains ", " smallest ", and " closed ", respectively.

Let there be a right angle ABC, r a line parallel to BC passing by A and s a line parallel to AB passing by C. Let D be the point of intersection of lines r and s ( Note that it has not been proven that D lies on the circle )

This proves that all points in the intersection are the same distance from the point E in the plane P, in other words all points in the intersection lie on a circle with center E. Note that OE is the axis of the circle.

( Note that if we use the nullary intersection convention, then there is no need to include X in the second definition.

Note that if t and u, t ≠ u are two values of the parameter then the intersection of the curves C < sub > t </ sub > and C < sub > u </ sub > is given by

Note however that it is not compositional with respect to the intersection operator.

Note that unlike possibility, fuzzy logic is compositional with respect to both the union and the intersection operator.

Note that, because a name translated to an address, which included a socket number as well as a node number, a name in AppleTalk mapped directly to a service being provided by a machine, which was entirely separate from the name of the machine itself.

Note that the number of points used in braille computing is not 6, but 8, as this allows the user, among other things, to distinguish between small and capital letters, as well as identify the position of the cursor.

Note that pure application of this method may provide only a partial ordering on the strings, since different strings can represent the same number ( as with " 2 " and " 2. 0 ", or when scientific notation is used, " 2e3 " and " 2000 ").

Note derivative is positive number | positive where green line appears, negative number | negative where red line appears, and zero ( number ) | zero where black line appears.

Note that the first element in a sequence has the index one and that $ refers to the length ( i. e. total number of elements ) of the sequence.

Note that reflection by a window is from the front side as well as the back side, and that some of the light bounces back and forth a number of times between the two sides.

It is unclear which version of the paradox is stronger .< ref group =" Note "> Let be the number of civilizations ( per unit volume ) that can be seen at a radius.

Note that due to the reduced number of colors in the image, there are obvious display issues. GIF is palette-based: the colors used in an image ( a frame ) in the file have their RGB values defined in a palette table that can hold up to 256 entries, and the data for the image refer to the colors by their indexes ( 0 – 255 ) in the palette table.

Like all subatomic particles, hadrons are assigned quantum numbers corresponding to the representations of the Poincaré group: J < sup > PC </ sup >( m ), where J is the spin quantum number, P the intrinsic parity ( or P-parity ), and C, the charge conjugation ( or C-parity ), and the particle's mass, m. Note that the mass of a hadron has very little to do with the mass of its valence quarks ; rather, due to mass – energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction.

Note that the maximum value of the angular momentum quantum number is limited by the principal quantum number: it can run only up to n − 1, i. e..

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: if the product resulting from the labor process is homogeneous ( all similar in quality and traits, for example, all cups of coffee ) then the value of the period ’ s product can be divided by the total number of items ( use-values ) produced to derive the unit value of each item.

Note: For any arbitrary number of propositional constants, we can form a finite number of cases which list their possible truth-values.

Note that the vertical scale, the number of digits, is a double logarithmic scale of the value of the prime.

Note: A number of other plants have been suggested by biblical scholars, e. g., Most notably Ginseng which looks similar to the mandrake root and has fertility enhancing properties, for which it was picked by Reuben in the Bible.

Note that s < sub > 0 </ sub > is now the sum of the weights and not the number of samples N.

Note that these statistics only show officially registered residents, and that the actual number of foreign citizens living in Shanghai is likely much higher.

Note derivative is positive number | positive where green, negative number | negative where red, and zero ( number ) | zero where black