Suppose that Alice and Bob had decided to measure spin along the x-axis.

Suppose Alice has a qubit in some arbitrary quantum state.

Suppose Alice has a qubit that she wants to teleport to Bob.

Suppose Alice wishes to communicate with Bob.

An example: Suppose that only Alice, Bob, and Carol have the keys to a bank safe and that, one day, the contents of the safe are missing ( without the lock being violated ).

Suppose Alice is playing limit Texas hold ' em and is dealt 9 ♣ 9 ♠ under the gun before the flop.

Suppose Alice and Bob want to resolve some dilemma via coin flipping.

Suppose Alice and Bob wish to communicate securely — they may choose to use cryptography.

Suppose Alice wants to prove her identity to Bob.

Suppose Bob wishes to send a message m to Alice whose public key is:

Suppose Alice and Bob wish to communicate.

Suppose that the number of puzzles sent by Bob is m, and it takes both Bob and Alice n steps of computation to solve one puzzle.

Suppose Bob and Alice start with a document containing the word Mary.

Suppose Bob wishes to send a message m to Alice:

Suppose then that Bob bids $ 2. 00 for the item.

Suppose that Bob bids again, this time at $ 2. 75.

Suppose Bob bids one more time, at $ 10. 00.

Suppose that Bob wants to buy a house a year from now.

Suppose Bob likes only chocolate, and Carol only vanilla.

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 that a speaker can have the concept of water we do only if the speaker lives in a world that contains H < sub > 2 </ sub > O.

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