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

Example: Suppose there are only three principles in our scientific theory about electrons ( those principles can be seen to be statements involving the properties ):

Suppose we want to transmit information about a source to the user with a distortion not exceeding D. Rate – distortion theory tells us that at least R ( D ) bits / symbol of information from the source must reach the user.

Suppose a psychologist proposes a theory that there are two kinds of intelligence, " verbal intelligence " and " mathematical intelligence ", neither of which is directly observed.

Suppose that the full action of the theory is given by the Einstein – Hilbert term plus a term describing any matter fields appearing in the theory.

: Suppose that a closed formula is a theorem of a first-order theory, where we denote.

Suppose that the minimal polynomial for T decomposes over F into a product of linear polynomials.

Suppose T = 2 sec (~ lunar distance ) then delta-phi = 8000 radians, i. e. ( 8000 * 180 )/ Pi.

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

Suppose we have an n-dimensional oriented Riemannian manifold, M and a target manifold T. Let be the configuration space of smooth functions from M to T. ( More generally, we can have smooth sections of a fiber bundle over M .)

Suppose the rod rotates at a constant rate so that the mass moves at speed v. Then the kinetic energy T of the mass is:

Suppose that x < sup > i </ sup > are local coordinates on the base manifold M. In terms of these base coordinates, there are fibre coordinates p < sub > i </ sub >: a one-form at a particular point of T * M has the form p < sub > i </ sub > dx < sup > i </ sup > ( Einstein summation convention implied ).

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.

First proof: Suppose forms a basis of ker T. We can extend this to form a basis of V:.

Suppose the set of objects is T =

Suppose G is a finitely generated group ; and T is a finite symmetric set of generators

Suppose that an L-formula True ( n ) defines T *.

Suppose that ( X, T ) is a topological space and that Σ is at least as fine as the Borel σ-algebra σ ( T ) on X.

Suppose X is a Tychonoff space, also called a T < sub > 3. 5 </ sub > space, and C ( X ) is the algebra of continuous real-valued functions on X.

If is closed, densely defined and continuous on its domain, then it is defined on B < sub > 1 </ sub >.< ref > Suppose f < sub > j </ sub > is a sequence in the domain of T that converges to.

Suppose X is the T × K matrix of explanatory variables resulting from T observations on K variables.

Suppose a pendulum is swinging with a particular period T. For such a system, it is advantageous to perform calculations relating to the swinging relative to T. In some sense, this is normalizing the measurement with respect to the period.

Suppose the available data consists of T iid observations

Suppose that S and T are two first-order theories.

Suppose that it takes twice as much capital per unit of output to produce trucks than it does to produce lasers, so that the capital cost per unit equals $ 20, 000 for trucks ( T ) and $ 10, 000 for lasers ( L ), where these coefficients are initially assumed not to change.

Suppose that T is a bounded operator on the normed vector space X.