# Suppose there exists a function called Insert designed to insert a value into a sorted sequence at the beginning of an array.

Suppose there is a chain at 1A, 2A, 3A, and 4A, along with another chain at 6A and 7A.

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 have N particles with quantum numbers n < sub > 1 </ sub >, n < sub > 2 </ sub >, ..., n < sub > N </ sub >.

Suppose that Y is the sum of n identically distributed independent random variables all with the same distribution as X.

Suppose a definition of a capacitor has an associated attribute called " Capacitance ", corresponding to the physical property of the same name, with a default value of " 100 pF " ( 100 picofarads ).

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 voters each decided to grant from 0 to 10 points to each city such that their most liked choice got 10 points, and least liked choice got 0 points, with the intermediate choices getting an amount proportional to their relative distance.

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 two curves γ < sub > 1 </ sub >: (- 1, 1 ) → M and γ < sub > 2 </ sub >: (- 1, 1 ) → M with γ < sub > 1 </ sub >( 0 )

:: “ 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 one wants to come up with a definition of " right " in the moral sense.

An uncountable subset of the real numbers with the standard ordering ≤ cannot be a well-order: Suppose X is a subset of R well-ordered by ≤.

Suppose for environmental reasons we needed to replace the chlorinated solvent, chloroform, with a solvent ( blend ) of equal solvency using a mixture of two non-chlorinated solvents from this table.

Suppose further, because this is necessary to the alleged case for our nuclear weapon as the defence of last resort, that, as in 1940, the United States was standing aloof from the contest but that, in contrast with 1940, Britain and the Warsaw Pact respectively possessed the nuclear weaponry which they do today.

Suppose that is a code word with fewer than non-zero terms.

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

Suppose the thimble were screwed out so that graduation 2, and three additional sub-divisions, were visible ( as shown in the image ), and that graduation 1 on the thimble coincided with the axial line on the frame.

Suppose that the thimble were screwed out so that graduation 5, and one additional 0. 5 subdivision were visible ( as shown in the image ), and that graduation 28 on the thimble coincided with the axial line on the sleeve.

Suppose that, instead of an exact observation, x, the observation is the value in a short interval ( x < sub > j − 1 </ sub >, x < sub > j </ sub >), with length Δ < sub > j </ sub >, where the subscripts refer to a predefined set of intervals.

Suppose there is a town with just one barber, who is male.

Suppose someone told you they had a nice conversation with someone on the train.

* 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.

Proof: Suppose that and are two identity elements of.

Suppose that K is a field ( for example, the real numbers ) and V is a vector space over K. As usual, we call elements of V vectors and call elements of K scalars.

Suppose that X is a non-singular n-dimensional projective algebraic variety over the field F < sub > q </ sub > with q elements.

Suppose that A is a set with a function w: A → N assigning a weight to each of the elements of A, and suppose additionally that the fibre over any natural number under that weight is a finite set.

) Suppose additionally that a < sub > n </ sub > is the number of elements of A with weight n. Then we define the formal Dirichlet generating series for A with respect to w as follows:

Suppose the group that is used has elements, where is the prime factorization of.

Suppose the Jacobian of the curve has elements and is the largest prime divisor of.

Suppose A is a unital *- algebra and O is a unital *- subalgebra whose self-adjoint elements correspond to observables.

Suppose V is an infinite dimensional vector space over a field F. If the dimension is κ, then there is some basis of κ elements for V. After an order is chosen, the basis can be considered an ordered basis.

Suppose you have a collection of lists, each node of a list contains an object, the name of the list to which it belongs, and the number of elements in that list.

Suppose the covariance matrix of is, where V is an n-by-n nonsingular matrix which was equal to in the more specific case handled in the previous section, ( where I is the identity matrix ,) but here is allowed to have nonzero off-diagonal elements representing the covariance of pairs of individual observations, as well as not necessarily having all the diagonal elements equal.

Suppose the scapegoat tree has elements and has just been rebuilt ( in other words, it is a complete binary tree ).

Suppose G is a finite group and U is a representation of G on a finite-dimensional complex vector space H. The action of G on elements of H induces an action of G on a vector subspace W of H in an obvious way:

Suppose X is a set of subspaces of H such that ( 1 ) the elements of X are permuted by the action of G on subspaces and ( 2 ) H is the ( internal ) algebraic direct sum of the elements of X, viz.

* Suppose that G is any doubly transitive permutation group on a set X with more than 2 elements.

Suppose further that for any n elements x < sub > 1 </ sub >,..., x < sub > n </ sub > of F which are linearly independent over Q, the extension field Q ( x < sub > 1 </ sub >,..., x < sub > n </ sub >, e ( x < sub > 1 </ sub >),..., e ( x < sub > n </ sub >)) has transcendence degree at least n over Q.

Suppose S is in a microstate indexed by m. From the above definitions, the total energy of the system S * is given by

Suppose n < sub > 1 </ sub >, n < sub > 2 </ sub >, …, n < sub > k </ sub > are positive integers which are pairwise coprime.

Unicity: Suppose satisfies, then by Theorem 1. 8,.

Player 1 moves first and chooses either F or U. Player 2 sees Player 1s move and then chooses A or R. Suppose that Player 1 chooses U and then Player 2 chooses A, then Player 1 gets 8 and Player 2 gets 2.

Suppose that one particle is in the state n < sub > 1 </ sub >, and another is in the state n < sub > 2 </ sub >.

Suppose that a certain slot machine costs $ 1 per spin and has a return to player ( RTP ) of 95 %.

Suppose a line runs through two points: P = ( 1, 2 ) and Q = ( 13, 8 ).

Suppose M is a C < sup > k </ sup > manifold ( k ≥ 1 ) and x is a point in M. Pick a chart φ: U → R < sup > n </ sup > where U is an open subset of M containing x.

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: