; 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 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 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 ).

) 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

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 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 ( A < sub > 1 </ sub >, φ < sub > 1 </ sub >) is an initial morphism from X < sub > 1 </ sub > to U and ( A < sub > 2 </ sub >, φ < sub > 2 </ sub >) is an initial morphism from X < sub > 2 </ sub > to U. By the initial property, given any morphism h: X < sub > 1 </ sub > → X < sub > 2 </ sub > there exists a unique morphism g: A < sub > 1 </ sub > → A < sub > 2 </ sub > such that the following diagram commutes:

Suppose a lossless antenna has a radiation pattern given by:

Suppose V and W are vector spaces over the field K. The cartesian product V × W can be given the structure of a vector space over K by defining the operations componentwise:

Suppose it is given that

Suppose we are given a closed, oriented curve in the xy plane.

Suppose that A, B, and C are the matrices representing the transformations T, S, and ST with respect to the given bases.

Suppose we are given a topological space X.

Suppose Ω is given in the standard form and let M be a 2n × 2n block matrix given by

Suppose on a given summer day the declination of the sun is + 20 °.

Suppose a stock price follows a Geometric Brownian motion given by the stochastic differential equation dS = S ( σdB + μ dt ).

Suppose we are given a Hidden Markov Model ( HMM ) with state space, initial probabilities of being in state and transition probabilities of transitioning from state to state.

Suppose we are given an element e < sub > 0 </ sub > ∈ E < sub > P </ sub > at P = γ ( 0 ) ∈ M, rather than a section.

Suppose S ' is in relative uniform motion to S with velocity v. Consider a point object whose position is given by r

Suppose that a tangent vector to the sphere S is given at the north pole, and we are to define a manner of consistently moving this vector to other points of the sphere: a means for parallel transport.

Suppose G and H are given as before, along with group homomorphisms

Suppose we are given a covariant left exact functor F: A → B between two abelian categories A and B.

Suppose a particle moves at a uniform rate along a line from A to B ( Figure 2 ) in a given time ( say, one second ), while in the same time, the line AB moves uniformly from its position at AB to a position at DC, remaining parallel to its original orientation throughout.