Suppose, says Searle, that this computer performs its task so convincingly that it comfortably passes the Turing test: it convinces a human Chinese speaker that the program is itself a live Chinese speaker.

Suppose that u and v are real-differentiable at a point in an open subset of, which can be considered as functions from to.

Suppose random variable X can take value x < sub > 1 </ sub > with probability p < sub > 1 </ sub >, value x < sub > 2 </ sub > with probability p < sub > 2 </ sub >, and so on, up to value x < sub > k </ sub > with probability p < sub > k </ sub >.

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 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 then that each player asks himself or herself: " Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?

* Suppose & B is equivalent to & D. If we acquire new information A and then acquire further new information B, and update all probabilities each time, the updated probabilities will be the same as if we had first acquired new information C and then acquired further new information D. In view of the fact that multiplication of probabilities can be taken to be ordinary multiplication of real numbers, this becomes a functional equation

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 further ," Socrates says, " that the man was compelled to look at the fire: wouldn't he be struck blind and try to turn his gaze back toward the shadows, as toward what he can see clearly and hold to be real?

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 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 each circle is a website, and an arrow is a link from one website to another, such that a user can click on a link within, say, website F to go to website B, but not vice versa.

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 the alternatives can be partitioned into subsets, where each subset has its own cost function, and each alternative belongs to only one subset.

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

Example: Suppose a supermarket wants to study buying habits of their customers, then using systematic sampling they can choose every 10th or 15th customer entering the supermarket and conduct the study on this sample.

# Suppose we have a spacetime that is globally hyperbolic, and two points and that can be connected by a timelike or null curve.

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

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

Suppose a differential equation can be written in the form

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 we have a two-state economy: the initial stock price can go either up to or down to.

Suppose a magnetic tape can support up to 3, 200 flux reversals per inch.

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

Suppose we have sample space.

) 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 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 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, 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 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 we have a material in its normal state, containing a constant internal magnetic field.

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