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: 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 acid can be the charged species and the conjugate base can be neutral in which case the generalized reaction scheme could be written as HA < sup >+</ sup > H < sup >+</ sup > + A.

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, however, that the fifth article did not completely deny perseverance of the saints ; Arminius, himself, said that " I never taught that a true believer can … fall away from the faith … yet I will not conceal, that there are passages of Scripture which seem to me to wear this aspect ; and those answers to them which I have been permitted to see, are not of such as kind as to approve themselves on all points to my understanding.

Note that wav files can also be encoded with the gsm codec.

Note that arrows between categories are called functors, subject to specific defining commutativity conditions ; moreover, categorical diagrams and sequences can be defined as functors ( viz.

Note that this is different from the recursive languages which can be decided by an always-halting Turing machine.

Note that for any fixed w the function f ( x ) = F ( w x ) is computable ; thus the universality property states that all computable functions of one variable can be obtained in this fashion.

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

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 ").

These polar unit vectors can be expressed in terms of Cartesian unit vectors in the x and y directions, denoted i and j respectively :< ref > Note: unlike the Cartesian unit vectors i and j, which are constant, in polar coordinates the direction of the unit vectors u < sub > r </ sub > and u < sub > θ </ sub > depend on θ, and so in general have non-zero time derivatives .</ ref >

Note that completeness is a property of the metric and not of the topology, meaning that a complete metric space can be homeomorphic to a non-complete one.

Note that this document type declaration can only appear after the optional XML declaration, and before the document body, if the document syntax conforms to XML.

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 if the operations are performed in a colour space where γ is not equal to 1 then the operation will lead to non-linear effects which can potentially be seen as aliasing artifacts ( or ' jaggies ') along sharp edges in the matte.

: Note that the equivalence relation generated in this manner can be trivial.

Note that one can also define a contravariant functor as a covariant functor on the dual category.

Note: Many of the essays found in these works have been individually translated and can be found in the English collections.

It is unclear which version of the paradox is stronger .< ref group =" Note "> Let be the number of civilizations ( per unit volume ) that can be seen at a radius.

Hunters use the clues to try to find the benchmark ; the benchmark can be logged as Found, Not Found, Note, or Destroyed.

Note that due to the reduced number of colors in the image, there are obvious display issues. GIF is palette-based: the colors used in an image ( a frame ) in the file have their RGB values defined in a palette table that can hold up to 256 entries, and the data for the image refer to the colors by their indexes ( 0 – 255 ) in the palette table.

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 the maximum value of the angular momentum quantum number is limited by the principal quantum number: it can run only up to n − 1, i. e..