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( Note that the empty set is considered finite, with cardinality zero.
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Note and empty
Note that the end tag's name is preceded by a slash character, "/", and that in empty elements the end tag is neither required nor allowed.
Note also that ' br ' is an empty element in that, while it may have attributes, it can take no content and it may not have an end tag.
Note that in the special case where A is the empty set the meet of A will be the greatest element of L. Likewise, the join of the empty set yields the least element.
Note that this is also true if the boundary is the empty set, e. g. in the metric space of rational numbers, for the set of numbers of which the square is less than 2.
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 ( x )< sub > 0 </ sub > = 1 because it is an empty product.
Note that may be much lower than the actual number of empty places in the queue, for example in the case where many producers have decremented it but are waiting their turn on before filling empty places.
Note that in both representations the empty product has cardinality 1.
Note that, if the empty list were the only base case, sorting a list with n entries would entail n + 1 quicksort calls that would do nothing but return immediately.
Note that empty cells do not imply that a particular language is lacking a word to describe the concept, but rather that the word for the concept in that language is formed from another stem and is not a cognate with the other words in the row.
Note that the empty set is a face of every simplex.
Note: the above table may incorrectly include the mass of the empty upper stage or stages.
Note: booby traps and improvised explosive devices frequently use plastic explosive as the booster charge, for example, some C4 or Semtex stuffed into the empty fuze pocket of a 120mm mortar shell.
Note also that functions do not in general attain a maximum value, and hence will in general not have an arg max: is the empty set, as x is unbounded on the real line.
Note that the rabbit on d2 can't be pushed to d1, c2, or d3, because those squares are not empty.
Note that an isometry is never strictly metric, except in the degenerate case of the empty space or a single-point space.
Note that the empty set belongs to every non-empty abstract simplicial complex, because it is a subset of every other set X in the complex.
Note that the unit element 1 corresponds to the empty canonical monomial.
Note removable disk pack s and empty covers on top of the drives
Note in particular the usage with an empty parameter — here the consecutive pipes mean that the first parameter passed to the template is the empty string.
Note that despite the name, in all of these situations, the void type serves as a unit type, not as a zero or bottom type, even though unlike a real unit type which is a singleton, the void type is said to comprise an empty set of values, and the language does not provide any way to declare an object or represent a value with type.
Note and set
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 a locally finite Borel measure automatically satisfies μ ( C ) < ∞ for every compact set C.
Note that the set of grammars corresponding to recursive languages is not a member of this hierarchy.
) 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.
The subgroup of generated by all commutators is called the derived group or the commutator subgroup of G. Note that one must consider the subgroup generated by the set of commutators because in general the set of commutators is not closed under the group operation.
Note that this definition cannot be expressed in the language of set theory itself.
Note, however, that the representation is not complete on the set of square-integrable functions.
* 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: Ringette distances itself from hockey as it has its own set of rules and is closely related to a mix of lacrosse and basketball.
Note that the term byte also had this ambiguity ; at one time, byte meant a set of bits but not necessarily 8.
Note that if the preorder is R < sup >+=</ sup >, S / ~ is the set of R-cycle equivalence classes: x ∈ if and only if x = y or x is in an R-cycle with y.
Note that the group of all permutations of a set is the symmetric group ; the term permutation group is usually restricted to mean a subgroup of the symmetric group.
( Note that in SQL the heading is not always a set of column definitions as described above, because it is possible for a column to have no name and also for two or more columns to have the same name.
Note that a sample of random variables ( i. e. a set of measurable functions ) must not be confused with the realizations of these variables ( which are the values that these random variables take, formally called random variates ).
* 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 ).
Note the concept of omnicausality in Abrahamic theology, which is the belief that God has set in motion all events at the dawn of time ; he is the determiner and the cause of all things.
A set T of real numbers ( red and green balls ), a subset S of T ( green balls ), and the infimum of S. Note that for finite set s the infimum and the minimum are equal.
The Note is introduced by the following words: " A preliminary note of explanation is being given to the Council Fathers from higher authority, regarding the Modi bearing on Chapter III of the Schema de Ecclesia ; the doctrine set forth in Chapter III ought to be explained and understood in accordance with the meaning and intent of this explanatory note.
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 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 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.
1.631 seconds.