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Page "Conceptual system" ¶ 9
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Note and notion
Note that when N = R, the map dφ < sub > x </ sub >: T < sub > x </ sub > M → R coincides with the usual notion of the differential of the function φ.
Note that this more general concept of boundedness does not correspond to a notion of " size ".
Note that this notion of image may not correspond to the usual notion of image, or range, of a function, even assuming that the morphisms in the category are functions.
Note When applied to normed spaces, the definitions in this section coincide with the notion of reflexivity for normed spaces.
Note that x does not have to be an element of S. This concept profitably generalizes the notion of a limit and is the underpinning of concepts such as closed set and topological closure.
Note Hume's use of the word number in the ancient sense, to mean a set or collection of things rather than the common modern notion of " positive integer ".
Note: In SGA4, tome I, section 1, the notion of left ( right ) exact functors have been defined for general categories, and not just abelian ones.
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 there are other notions of compactness in mathematics ; also, the term " finite " in its normal set theoretic meaning does not coincide with the order-theoretic notion of a " finite element ".
Note that there is no notion of a group action in this sense.
Note from the earlier discussion of representation that both the Churchlands ' connectionist systems and Fodor's symbolic systems use this notion of computation.
Note, however, that while the notion of an association scheme generalizes the notion of a group, the notion of a commutative association scheme only generalizes the notion of a commutative group.
Note that the polarization direction is perpendicular to the wires ; the notion that waves " slip through " the gaps between the wires is incorrect.

Note and is
( 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.

Note and different
( Note, however, that a GC stacking interaction with the next base pair is geometrically different from a CG interaction.
Note that this is different from the recursive languages which can be decided by an always-halting Turing machine.
Note that the points must all be different numbers for them to count towards the fire bet.
: Note: Individual casinos may pay some of these bets at different payout ratios than those listed below.
Years are usually counted from a particular starting point, usually called the epoch, with era referring to the particular period of time ( Note the different use of the terms in geology ).
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: This study only involved male subjects which may be significant as sex steroids may have different effects in the responses to cortisol administration.
Note: In Australia, this is different.
Note that this is different from the original Elfengold published by White Wind.
Note that the aspectual systems of certain dialects of English, such as African-American Vernacular English ( see for example habitual be ), and of creoles based on English vocabulary, such as Hawaiian Creole English, are quite different from those of standard English, and often distinguish aspect at the expense of tense.
Methods PUT and DELETE are defined to be idempotent, meaning that multiple identical requests should have the same effect as a single request ( Note that idempotence refers to the state of the system after the request has completed, so while the action the server takes ( e. g. deleting a record ) or the response code it returns may be different on subsequent requests, the system state will be the same every time ).
Note the map indicates the contemporary coast lines, which are different, in parts of the English Channel and the North Sea, from those of Roman Britain.
Note that the orange circles appear of different sizes, even though equal.
Note that different requirements apply to the other related concepts ( cryptographic hash functions, checksums, etc.
: is a spherical harmonic function of degree ℓ and order m. Note that the generalized Laguerre polynomials are defined differently by different authors.
Note the different check digits in each.
( Note: this study-cycle follows a different schedule than the regular one ; contains extensive archives in English ).
( Note: Astronomy should not be confused with astrology, which assumes that people's destiny and human affairs in general are correlated to the apparent positions of astronomical objects in the sky -- although the two fields share a common origin, they are quite different ; astronomers embrace the scientific method, while astrologers do not.
Note this does not restrict dormant forms of life to these environments, so this argument only contradicts the widest interpretation of panspermia — that life is ongoing and is spread across many different environments throughout the Universe — and presupposes that any life needs those elements, which the proponents of alternative biochemistries do not consider certain.
Note that " secure " here has a precise mathematical meaning, and there are multiple different ( meaningful ) definitions of what it means for an encryption scheme to be " secure ".
Note that an eight-dimensional vector can be specified in many different ways depending on what basis is chosen for the space.
Note that the term " automatic revolver " has two different meanings.
* The probability a set will have features different and features the same is ( Note: d = 0 all four features the same is impossible as no two cards are identical ).

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