Note-that-the-third-axiom-is-actually-redundant

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Note and third

Note that sometimes the elliptic integral of the third kind is defined with an inverse sign for the characteristic,

* Note: The original release of this set included Godzilla vs. Megalon, which was replaced with The Giant Gila Monster after Rhino attempted to license the film from a third party which had no claim to the movie.

Note also the pervasive pattern of alliteration, where the first and / or second stress alliterate with the third, but not with the fourth.

Note that some sources switch the numbering of the second and third theorems.

Note that a category is called preadditive if just the second holds, whereas it is called semiadditive if both the first and the third hold.

Note that the above equation is flawed — as the temperature approaches zero, the entropy approaches negative infinity, in contradiction to the third law of thermodynamics.

Note that one region includes all of the Americas ; a second includes all of Europe and Africa, plus all of Russia, and the third region includes all of Asia outside of Russia, plus Australia and New Zealand.

Note that in the eight precepts, the third precept on sexual misconduct is made more strict and becomes a precept of celibacy.

Note well that only the first nine arguments are by Dionysius — arguments 10 to 16 as well as the second paragraphs of 3 and 4 and the third paragraph of 9 are later interpolations.

Note that the vertex degrees must be finite, but need not be bounded: it is possible to have one vertex of degree 10, another of degree 100, a third of degree 1000, and so on.

Note that it is not always advantageous to the company to price discriminate even if it is possible, especially for second and third degree discrimination.

Note: Commonly called the Five Precepts or Five Principles, they start in the third column from the right below the space, and continue in the fourth and fifth columns from the right.

Note that Pinyin uses the caron, not the breve, to indicate the third tone of Mandarin Chinese ; the breve cannot be used as a substitute in computer environments because Unicode does not provide an equivalent of ǚ with a breve.

Note that for skewness and kurtosis alternative definitions exist, which are based on the third and fourth cumulant respectively.

Ian Brown used a passage from Elizabeth's poem A Musical Note to name his third solo album The Music of the Spheres.

Note that there is a third possibility in the above scenario ; the hedge fund could decide to liquidate its position after a certain period of time in an attempt to realise its gains or losses.

* Il secondo libro de madrigali ( Venice 1564 ; five voices ) ( Note that the third book was published before the second )

Note that the first element in the minimum corresponds to insertion ( from to ), the second to deletion and the third to match or mismatch, depending on whether the respective symbols are the same.

Note that since the local name has been output, the scope of is extended to cover the third component as well.

The two winners came back on the third week, playing Melody Roulette, Sing a Tune, and Bid a Note for 10 points each, and Golden Medley Showdown for 30, to determine the $ 100, 000 winner.

Note that " an innings " can mean either a particular side's innings ( Sri Lanka made 464 in the third innings the game ) or that of both sides ( England had the better of the first innings, outscoring Australia by 104 ), the difference being understood by context.

After the third Wilson Note of 24 October, General Ludendorff suddenly changed his mind and declared the conditions of the allies to be unacceptable.

But after the third Wilson Note, many soldiers and the general population believed that Emperor Wilhelm II had to abdicate in order to achieve peace.

Note and axiom

**** 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 there is one axiom for every such predicate φ ; thus, this is an axiom schema.

Note that the existence of the Cartesian product can be proved without using the power set axiom, as in the case of the Kripke – Platek set theory.

Note that there is no corresponding axiom of intersection.

Note that modern set-theoretic definitions usually define operations as maps between sets, so adding closure to a structure as an axiom is superfluous, though it still makes sense to ask whether subsets are closed.

It is then a theorem that there are in fact infinitely many such lines through P. Note that this axiom still does not uniquely characterize the hyperbolic plane uniquely up to isometry ; there is an extra constant, the curvature K < 0, which must be specified.

Note how, applying the reduction substitution axiom, occurrences of are now labeled as.

) Note that even without such an axiom we could form the first n terms of such a sequence, for any natural number n ; the axiom of dependent choices merely says that we can form a whole sequence this way.

Note that in this case, the axiom of extensionality must be formulated to apply only to objects that are not urelements.

Note that the translation axiom implies Ta =

Note also that there exists a number of alternative axiomatizations of S5 which do not employ the axiom 5 ( of course, 5 remains a theorem of S5 independently of a given axiomatization ).

Note that an everywhere defined extension exists for every operator, which is a purely algebraic fact explained at Discontinuous linear map # General existence theorem and based on the axiom of choice.

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.

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