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Page "Quaternions and spatial rotation" ¶ 96
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Suppose and however
Suppose, however, that you pick two tickets rather than one.
Suppose, however, that the course was pass / fail and students were required to score above 70 on both tests to pass.
Suppose, however, that we pass over this objection ; how does Peacock lay the foundation for general algebra?
Suppose, however, for a moment, all existing space to be bounded, and that a man runs forward to the uttermost borders, and stands upon the last verge of things, and then hurls forward a winged javelin ,— suppose you that the dart, when hurled by the vivid force, shall take its way to the point the darter aimed at, or that something will take its stand in the path of its flight, and arrest it?

Suppose and we
Suppose the lines in front of the movie houses were too long and we couldn't get in??
Suppose, he says, that the tables were turned, and we were in the Soviets' position: `` There would be more than 2,000 modern Soviet fighters, all better than ours, stationed at 250 bases in Mexico and the Caribbean.
Suppose we do get our fears out in the open, what then??
Suppose we have sample space.
Suppose we now consider a slightly more complicated vector field:
Suppose that we had a general decision algorithm for statements in a first-order language.
Suppose we wish to make it display the next available buffer.
Suppose we wanted to define the phrase human being.
Suppose we look at S1 just a couple of years after it was built.
Suppose that a speaker can have the concept of water we do only if the speaker lives in a world that contains H < sub > 2 </ sub > O.
Suppose we have N particles with quantum numbers n < sub > 1 </ sub >, n < sub > 2 </ sub >, ..., n < sub > N </ sub >.
Suppose we have a system of N bosons ( fermions ) in the symmetric ( antisymmetric ) state
Suppose a number of scientists are assessing the probability of a certain outcome ( which we shall call ' success ') in experimental trials.
Suppose the state of a quantum system A, which we wish to copy, is ( see bra-ket notation ).
Suppose we start with one electron at a certain place and time ( this place and time being given the arbitrary label A ) and a photon at another place and time ( given the label B ).
Suppose, for concreteness, that we have an algorithm for examining a program p and determining infallibly whether p is an implementation of the squaring function, which takes an integer d and returns d < sup > 2 </ sup >.
Suppose we have a material in its normal state, containing a constant internal magnetic field.
Suppose, for example, we are interested in the set of all adult crows now alive in the county of Cambridgeshire, and we want to know the mean weight of these birds.
Suppose, for example, we are interested in the set of all adult crows now alive in the county of nederlands best country, and we want to know the mean weight of these birds.
Suppose we wish to deny that we can understand what an actual infinity is, and therefore we cannot understand what ( God's ) eternity is.
Suppose we integrate the inhomogeneous wave equation over this region.

Suppose and have
) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is
; Dennett's reply from natural selection: Suppose that, by some mutation, a human being is born that does not have Searle's " causal properties " but nevertheless acts exactly like a human being.
Suppose both ISPs have trans-Atlantic links connecting their two networks, but A < nowiki >' s </ nowiki > link has latency 100 ms and B's has latency 120 ms.
Suppose that you add blue, then the blue – red – black tree defined like red – black trees but with the additional constraint that no two successive nodes in the hierarchy will be blue and all blue nodes will be children of a red node, then it becomes equivalent to a B-tree whose clusters will have at most 7 values in the following colors: blue, red, blue, black, blue, red, blue ( For each cluster, there will be at most 1 black node, 2 red nodes, and 4 blue nodes ).
Suppose a person states ; " I believe that trinini exist, but I have absolutely no idea of what trininis are.
Suppose that we have already constructed Lebesgue measure on the real line: denote this measure space by ( R, B, λ ).
Suppose it is also known that 75 % of women have long hair, which we denote as
Suppose then that n observations have been made
* Suppose that is a sequence of Lipschitz continuous mappings between two metric spaces, and that all have Lipschitz constant bounded by some K. If ƒ < sub > n </ sub > converges to a mapping ƒ uniformly, then ƒ is also Lipschitz, with Lipschitz constant bounded by the same K. In particular, this implies that the set of real-valued functions on a compact metric space with a particular bound for the Lipschitz constant is a closed and convex subset of the Banach space of continuous functions.
* Suppose we have a language L recognized by both the RP algorithm A and the ( possibly completely different ) co-RP algorithm B.
Suppose we have a preparation procedure for a system in a physics
Suppose further that in order to find another dozen articles of interest, the researcher would have to go to an additional 10 journals.
Suppose we have K electronic eigenfunctions of, that is, we have solved
Suppose that we have pages: de: Zug,: en: Train and: fr: Train, then we need:
Suppose that you have a coin purse containing five quarters, five nickels and five dimes, and one-by-one, you randomly draw coins from the purse and set them on a table.
Suppose that after a while the mathematician in question settled on the new conjecture " All shapes that are rectangles and have four sides of equal length are squares ".
Suppose a " low density residential " zone requires that a house have a setback ( the distance from the edge of the property to the edge of the building ) of no less than 100 feet ( 30 m ).
Suppose you have a function

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