:: “ 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 that Af, and that the average operation requires only Af sec..

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 that is the risk-free interest rate to expiry of the domestic currency and is the foreign currency risk-free interest rate ( where domestic currency is the currency in which we obtain the value of the option ; the formula also requires that FX rates – both strike and current spot be quoted in terms of " units of domestic currency per unit of foreign currency ").

Suppose that F: U → Y is Gâteaux differentiable at each point of the open set U. One notion of continuous differentiability in U requires that the mapping on the product space

Suppose we have a password hash function H and a finite set of passwords P. The goal is to precompute a data structure that, given any output h of the hash function, can either locate an element p in P such that H ( p ) = h, or determine that there is no such p in P. The simplest way to do this is compute H ( p ) for all p in P, but then storing the table requires Θ (| P | n ) bits of space, where n is the size of an output of H, which is prohibitive for large P.

Suppose that whenever P ( β ) is true for all β < α, then P ( α ) is also true ( including the case that P ( 0 ) is true given the vacuously true statement that P ( α ) is true for all ).

Suppose it is also known that 75 % of women have long hair, which we denote as

* 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 that L is a lattice of determinant d ( L ) in the n-dimensional real vector space R < sup > n </ sup > and S is a convex subset of R < sup > n </ sup > that is symmetric with respect to the origin, meaning that if x is in S then − x is also in S.

A video was also filmed for " Someday I Suppose " and it received minor airplay on MTV.

Suppose also that he thinks that it is not ethical to stone people to death merely for being Wiccan.

Suppose also another polynomial exists also of degree at most n that also interpolates the n + 1 points ; call it q ( x ).

Suppose, a mutual fund that holds shares of the company sells warrants against those shares, also exercisable at $ 500 per share.

The theorem can also be used to deduce that the domain of a non-constant elliptic function f cannot be C. Suppose it was.

Suppose a rich and powerful actor is also a drug addict.

The covariant derivative can also be constructed from the Cartan connection η on P. In fact, constructing it in this way is slightly more general in that V need not be a fully fledged representation of G. Suppose instead that that V is a (, H )- module: a representation of the group H with a compatible representation of the Lie algebra.

Suppose also that the series

Suppose also, M contains the identity operator on H.

Suppose we define thermodynamic conjugate quantities as, which can also be expressed as linear functions ( for small fluctuations ):

Suppose that F is a ( 1-dimensional ) formal group law over R. Its formal group ring ( also called its hyperalgebra or its covariant bialgebra ) is a cocommutative Hopf algebra H constructed as follows.

Suppose S is an immersed submanifold of M. If the inclusion map i: S → M is closed then S is actually an embedded submanifold of M. Conversely, if S is an embedded submanifold which is also a closed subset then the inclusion map is closed.

Suppose we have a path-connected space X, covered by path-connected open subspaces A and B whose intersection is also path-connected.

Suppose we want to add the two arrays x and y and also do something depending on the variable w. We have the following C code:

Suppose also that at most one person belongs to the intersection of any two committees.

Suppose also that, in the plane α ′, a definite side of the straight line a ′ be assigned.

Suppose both of them have at present the same price yield ( p-y ) combination ; also you have to take into consideration the profile, rating, etc.

Suppose also that

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

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 that the government finances some extra spending through deficits ; i. e. it chooses to tax later.

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

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 ).