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Page "Algebraic data type" ¶ 83
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Note and we
Note that we need not know the value of p, for the experiment to be binomial.
Note that if we regard the product as a vector space, then B is not a linear transformation of vector spaces ( unless or ) because, for example.
Note that after calling, we are left with a function that takes a single argument and returns another function, not a function that takes two arguments.
( Note that we are imagining the vector field to be like the velocity vector field of a fluid ( in motion ) when we use the terms flow, sink and so on.
Note that by reversing the equation, we can swap < math > < </ math > and, for example:
Alice now discards three of her own cards, and replaces them with three from the top of the deck ( Note: in a player-dealt casino game there is often a rule that the dealer must discard before picking up the deck, but this is a home game so we won't worry about such details ).
Note that we ignored the quotient in each step except to notice when the remainder reached 0, signalling that we had arrived at the answer.
) Note that we have omitted the Π < sub > j </ sub > n < sub > j </ sub > term, because each single-particle state can appear only once in a fermionic state.
Note that we have to restrict the sum to ordered values of m < sub > 1 </ sub >, ..., m < sub > N </ sub > to ensure that we do not count each multi-particle state more than once.
Note: For any arbitrary number of propositional constants, we can form a finite number of cases which list their possible truth-values.
#* Note: This fact provides a proof of the infinitude of primes distinct from Euclid's Theorem: if there were finitely many primes, with p being the largest, we reach an immediate contradiction since all primes dividing 2 < sup > p </ sup > − 1 must be larger than p .</ li >
Note: In cases where the optical design of a microscope produces an appreciable lateral separation of the two beams we have the case of classical interference microscopy, which does not result in relief images, but can nevertheless be used for the quantitative determination of mass-thicknesses of microscopic objects.
: Note this model assumes the particle is a point mass, which is certainly known to be false in many cases in which we use this model ; for example, as a model of planetary motion.
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 that we require the domains of G < sub > 2 </ sub >, G < sub > 3 </ sub > to be broad enough to make the above properties meaningful.
Note we have g ( 1 ) = 1.
Note that here we are not concerned about the number of computational steps, or the size of the computer memory used.
Note that the shells exist for both protons and neutrons individually, so that we can speak of " magic nuclei " where one nucleon type is at a magic number, and " doubly magic nuclei ", where both are.
A subset T is totally ordered if for any s, t in T we have s ≤ t or t ≤ s. Such a set T has an upper bound u in P if t ≤ u for all t in T. Note that u is an element of P but need not be an element of T. An element m of P is called a maximal element ( or non-dominated ) if there is no element x in P for which m < x.
Note that, if the language is infinite, the enumerating algorithm provided can be chosen so that it avoids repetitions, since we can test whether the string produced for number n is " already " produced for a number which is less than n. If it already is produced, use the output for input n + 1 instead ( recursively ), but again, test whether it is " new ".

Note and must
Note that the points must all be different numbers for them to count towards the fire bet.
Note that is a monotone function in γ and that the solution γ must satisfy.
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 a dominatrix does not necessarily dominate a male partner ; a dominatrix may well have female submissives, nor must the role of a dominatrix involve pain toward the submissive ; her domination can be verbal, involving humiliating tasks and servitude.
Note that polystyrene peanuts must be used ; biodegradable packing peanuts will decompose into a sludge.
( Note: In the above calculation, the square-root, must be positive.
Note: In children there must be evidence of the capacity for age-appropriate social relationships with familiar people and the anxiety must occur in peer settings, not just in interactions with adults.
Note that in the case of hybrid offences, the Crown must make a binding decision as to whether to proceed summarily or by indictment prior to the defendant making his or her plea.
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 ).
Note that any element of I must have the form αω, by virtue of our assumption that.
( Note that the boiling point of water varies with pressure, so this must be controlled.
Note 1: A duplexer must be designed for operation in the frequency band used by the receiver and transmitter, and must be capable of handling the output power of the transmitter.
Note 2: A duplexer must provide adequate rejection of transmitter noise occurring at the receive frequency, and must be designed to operate at, or less than, the frequency separation between the transmitter and receiver.
Note 3: A duplexer must provide sufficient isolation to prevent receiver desensitization.
Note that the earth itself has no role in this fault-clearing process since current must return to its source, not the earth as is sometimes believed ( see Kirchhoff's circuit laws ).
Note: must be positive.
Note that the arguments of the binomial coefficient are decremented due to order: the last " failure " must occur last, and so the other events have one fewer positions available when counting possible orderings.
Note that is the location to jump to, not the address of a handler, and so must be skipped () whether or not the branch is taken.
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 that if a < sub > 2 </ sub > were non-zero there would be no way to cancel the M value — therefore a < sub > 2 </ sub > must be zero.

Note and also
Note also that if Af, then Af is divisible by the polynomial p, because Af contains each Af as a factor.
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 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 also that antibodies tend to discriminate between the specific molecular structures presented on the surface of the antigen ( as illustrated in the Figure ).
Note the confident local allusion in 19: 9 to " the school of Tyrannus " and in 19: 33 to " Alexander "; also the very minute topography in 20: 13 – 15.
Note that wav files can also be encoded with the gsm codec.
Note that t < sup > 0 </ sup > = 1, ( 1 − t )< sup > 0 </ sup > = 1, and that the binomial coefficient,, also expressed as or is:
Note that traditional Berkeley DB also supports a Java API, but it does so via JNI and thus requires an installed native library.
* * Note: this is also the westernmost point of Africa
Note also Mirbt, Quellen, 2d ed, pp. 202 – 255.
Note also that the terms are not always treated as mutually exclusive ; there is not necessarily anything contradictory in the statement that " the language of the Pennsylvania Dutch is a dialect of German ".
Note also that even in validating SGML or XML 1. 0 or XML 1. 1 parsers, the external entities referenced by an FPI and / or URI in declared notations are not retrieved automatically by the parsers themselves.
Note that it is also possible to tunnel DPNSS and its associated PCM ( G711 ) over an IP network.
Note that also depends on.
Cultured skin and prostate cancer cells showed significant mortality ( compared to nonmalignant cells ) when treated with a combination of quercetin and ultrasound Note that ultrasound also promotes topical absorption by up to 1, 000 times, making the use of topical quercetin and ultrasound wands an interesting proposition.
Note that one can also define a contravariant functor as a covariant functor on the dual category.
* Note: 12ZTAX22 also came as a limited edition with a box designed to contain all the Rage Hard UK issues ( box featured the Red fist )
Note also that until well into the 20th Century, rather than an official readying the ball for scrimmage, the side entitled to the snap had complete custody of the ball and could snap it from the required spot at any time ; for instance, a tackled ball carrier might feign injury, then suddenly snap the ball while recumbent, there being no stance requirement yet.
Note that purnima or pornima is Sanskrit for full moon, which has also become the Malay word for full moon purnama.
Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).
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: see also for the original pretranslation text of this council in Greek and Latin )
Note that self-splicing introns are also sometimes found within tRNA genes.
Note also the existence of yank — the derivative of force with respect to time.
Note: There was also an experimental KV-1K-Katyusha mounted on KV-1 tank which was not taken in service.

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