Suppose that a further percent of the citizens also vote on every issue in the local government ballots.

Example: Suppose the government were to cut taxes.

; 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 the formula for some given function is known, but too complex to evaluate efficiently.

It is frequently stated in the following equivalent form: Suppose that is continuous and that u is a real number satisfying or Then for some c ∈ b, f ( c ) = u.

Suppose Alice has a qubit in some arbitrary quantum state.

# Suppose that P is some piece of knowledge.

:: “ Suppose that a sheriff were faced with the choice either of framing a Negro for a rape that had aroused hostility to the Negroes ( a particular Negro generally being believed to be guilty but whom the sheriff knows not to be guilty )— and thus preventing serious anti-Negro riots which would probably lead to some loss of life and increased hatred of each other by whites and Negroes — or of hunting for the guilty person and thereby allowing the anti-Negro riots to occur, while doing the best he can to combat them.

Suppose block M is a dominator with several incoming edges, some of them being back edges ( so M is a loop header ).

* 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 some given data points each belong to one of two classes, and the goal is to decide which class a new data point will be in.

Suppose M is some 2-dimensional Riemannian manifold ( not necessarily compact ), and we specify a " triangle " on M formed by three geodesics.

Suppose we are given boundary conditions, i. e., a specification of the value of φ at the boundary if M is compact, or some limit on φ as x approaches ∞.

Suppose that one has a table listing the population of some country in 1970, 1980, 1990 and 2000, and that one wanted to estimate the population in 1994.

Suppose homo economicus thinks about exerting some extra effort to defend the nation.

Suppose some particle has a mass m which is 3. 4 times the mass of electron.

Suppose, however, that we have some matrix Q that is not a pure rotation — due to round-off errors, for example — and we wish to find the quaternion q that most accurately represents Q.

Suppose two people who once loved each other come to be on bad terms ; they must make some condition of reconciliation before the love they previously enjoyed can be revived.

Suppose we can use some number, to index the quality of used cars, where is uniformly distributed over the interval.

Suppose that hunting requires also some arrows, with input coefficients equal to, meaning that to catch for instance one beaver you need to use arrows, besides hours of labour.

Suppose that ζ is an th root of unity for some odd prime.

Suppose that ζ is an lth root of unity for some odd regular prime l. Since l is regular, we can extend the symbol

Suppose for some unknown constants and unobserved random variables, where and, where < math > k < p </ math >, we have

Suppose some theory T implies an observation O ( observation meaning here the result of the observation, rather than the process of observation per se ):

Suppose that we have statements, denoted by some formal sequence of symbols, about some objects ( for example, numbers, shapes, patterns ).

Suppose we replace the real Hamiltonian of the model by a trial Hamiltonian, which has different interactions and may depend on extra parameters that are not present in the original model.

Suppose a single extra pair of identical traders is added to this initial pair.

Suppose further that recipients of the new spending by the builder in turn spend their new income, this will raise demand and possibly consumption further, and so on.

Suppose a line runs through two points: P = ( 1, 2 ) and Q = ( 13, 8 ).

Suppose that we are sending messages through the channel with index ranging from to, the number of distinct possible messages.

Suppose we interpolate through n + 1 data points with an at-most n degree polynomial p ( x ) ( we need at least n + 1 datapoints or else the polynomial cannot be fully solved for ).

Given a circle k, with a center O, and a point P outside of the circle, we want to construct the ( red ) tangent ( s ) to k that pass through P. Suppose the ( as yet unknown ) tangent t touches the circle in the point T. From symmetry, it is clear that the radius OT is orthogonal to the tangent.

Suppose that the sum of the two input signals is applied to a diode, and that an output voltage is generated that is proportional to the current through the diode ( perhaps by providing the voltage that is present across a resistor in series with the diode ).

Suppose f is the cubic polynomial vanishing on the three lines through AB, CD, EF and g is the cubic vanishing on the other three lines BC, DE, FA.

Suppose a tunnel is dug from one end of the earth to the other end straight through the center of earth, a stone dropped in such a tunnel oscillates with Schuler's time constant.

Suppose that the result of the measurement is that the photon passes through the filter.

:" Suppose that this wire, which we may take to be part of a grid, is made still more negative with a view to controlling the current through the tube.

Midway through the text, Abbey observes that nature is something lost since before the time of our forefathers, something that has become distant and mysterious which he believes we should all come to know better: " Suppose we say that wilderness provokes nostalgia, a justified not merely sentimental nostalgia for the lost America our forefathers knew.

Suppose that M is a smooth manifold containing a point p. We shall define the jets of curves through p, by which we henceforth mean smooth functions such that f ( 0 )= p.

Suppose that the equivalence problem has been through the loop enough times that no further reduction is possible.

Suppose company A manufactures down to 130 nm, while company B manufactures down to 22 nm, by extending its photolithography capability through years of successive resolution enhancements, such as wavelength change ( i. e., from 248 nm to 193 nm ), more and more aggressive optical proximity correction, more and more costly phase-shift masks, converting to immersion lithography and finally, implementing double patterning.

Suppose some configuration of charges ( may be non-stationary ) produce an electric field in some direction, then rotating the configuration of the charges ( without disturbing the internal dynamics that produces the particular field ) will lead to a net rotation of the direction of the electric field. These two properties are interconnected through the more general property that rotating any system of charges causes a corresponding rotation of the electric field.