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 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, 6 and 8 lock levers don't require holes for contacts.

Note that the validity of a conditional proof does not require that the CPA is actually true, only that if it is true it leads to the consequent.

Note that this does not require 100 % awareness from the onset of the data warehousing effort, no master plan is required upfront.

Note the systems mentioned typically require carabineers and the use of multiple useful knots.

Note that these arguments may indeed have validity, but they require some independent justification of the connection between their terms: otherwise the argument ( as a logical tool ) remains fallacious.

Note that the non-inverting input of the operational amplifier will need a path for DC to ground ; if the signal source might not give this, or if that source requires a given load impedance, the circuit will require another resistor — from input to ground.

Note that the Schwarzschild metric describes an idealized black hole that exists eternally from the perspective of external observers ; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric.

* Global homepage Note: some pages require CAcert. orgs root certificate which is not included with many web browsers.

Note that unlike the other two formulae ( the Euler product and the divisor sum ) this one does not require knowing the factors of n.

Note that, because of the overhead from determining nearest neighbor pairs, exact resolution of long-range, compared with particle size, forces can increase computational cost or require specialized algorithms to resolve these interactions.

Note that Dirichlet's theorem does not require the prime numbers in an arithmetic sequence to be consecutive.

Note that any travel off the main highways require a tribal recreation permit, available from the San Carlos Recreation and Wildlife department, and at local convenience and sporting-goods stores.

( Note that several of these beaches are restricted to owners only, and those designated as public require a beach pass.

Note that this program is able to generate its index from information built in to the program ; it does not require any external resources in order to find the index.

Note that unlike Judeo-Christian religions Shinto due to its nature does not require the same admission of faith, instead merely participating in certain aspects of Shinto is generally considered enough for association.

Note that while CRTs, plasma screens, and organic light-emitting diode displays generate their own light, liquid crystal displays ( LCDs ) like TFT screens require a backlight of either cold cathode fluorescent lamps or, more often today, LEDs.

Note that many tools make a distinction between Business Rules Engines and Business Rules Management, and require a translation between the two.

Note that contrary to the standard misconception, the Eddington limit does not require spherical symmetry.

Note that all official NHRA records require a " back-up " ( speed and elapsed time within 1 % of the record ) run to verify the newer, higher level of performance.

Note that the maximally extended Schwarzschild metric describes an idealized black hole / white hole that exists eternally from the perspective of external observers ; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric.

Note that one may need to require ' to be absolutely integrable with respect to the weight ' in order for this integral to be finite.

Note, these states explicitly require licensing for card issuers.

Note: in order for the FT to be valid we require that.

Note that just because a living fossil is a surviving representative of an archaic lineage does not necessarily require that it retains all of the " primitive " features ( plesiomorphies ) of the lineage it is descended from ; that is, they may possess one to many derived features ( autapomorphies ), that have evolved since the time of their lineage's divergence.