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 chocolate pictured here is soft, can easily be crumbled by hand, and already has sugar added.

* * Note: Guinea-Bissau does not have a northern-most point, the border here being formed by a straight horizontal line

Note that chair does not change form between " the chair is here " ( subject ) and " I saw the chair " ( direct object ), a distinction made by word order and context.

Note: These totals include some foreign-owned ships registered here as a flag of convenience: Denmark 13 ( 2002 est.

Note that here, the same value of γ remains unchanged.

Note that zero, which is not needed in the other systems, is of crucial importance here, in order to be able to " skip " a power.

Note that pot odds do not matter in this situation, because the factor here is whether it is more profitable to raise or call, rather than to call or fold.

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 the set-theoretic union, in some contexts closely related to logical disjunction ( or ), is used here for sets of statements in such a way that it is more related to logical conjunction ( and ).

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 that the waves shown here are real for illustrative purposes only whereas, in quantum mechanics the wave function is generally complex.

Note that the re-visiting policies considered here regard all pages as homogeneous in terms of quality (" all pages on the Web are worth the same "), something that is not a realistic scenario, so further information about the Web page quality should be included to achieve a better crawling policy.

( Note: the word " trapezohedron " as used here and in most mineral texts refers to the shape called a Deltoidal icositetrahedron in solid geometry.

Note that here Latin indices denote the " Lorentzian " vierbein labels while Greek indices denote manifold coordinate indices.

Note that the term Iranian as used here is a linguistic term and does not refer to the nation of Iran.

The path loss for the first ten kilometers may be 150 -- 190 dB ( Note: These values are very approximate and are given here only as an illustration of the range in which the numbers used to express the path loss values can eventually be, these are not definitive or binding figures -- the path loss may be very different for the same distance along two different paths and it can be different even along the same path if measured at different times.

" Note here the allusion to the tradition of mumming, Morris dancing and wedding celebrations at Pentecost.

Note that the Bernstein-von Mises theorem asserts here the asymptotic convergence to the " true " distribution because the probability space corresponding to the discrete set of events is finite ( see above section on asymptotic behaviour of the posterior ).

( Note that it is written as a relation, not as a function: T isn't written here as a function of M, L, and g .)

( Note: Although the term " winter squash " is used here to differentiate from " summer squash ", it is also commonly used as a synonym for Cucurbita maxima.

2 < sup >( Exponent − Exponent Bias )</ sup > × 1. Significand – Note the Significand must not be converted to decimal here

Note that the remains of United States soldiers were not buried here.

Note that commutativity is crucial here ; it ensures that the sum of two group homomorphisms is again a homomorphism.

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 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 ".