If two players tie for minority, they will share the minority shareholder bonus. Suppose Festival is the chain being acquired.

Proof: Suppose that and are two identity elements of.

Proof: Suppose that and are two inverses of an element of.

Suppose that on these sets X and Y, there are two binary operations and that happen to constitute the groups ( X ,) and ( Y ,).

Suppose, for example, that two particles interact.

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

: Suppose that we know we are in one or other of two worlds, and the hypothesis, H, under consideration is that all the ravens in our world are black.

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, however, that you pick two tickets rather than one.

Suppose there is a sequence of independent Bernoulli trials, each trial having two potential outcomes called “ success ” and “ failure ”.

Suppose that there are two agents in an economy, one that only values guns and one that only values butter.

Suppose you want to find the shortest path between two intersections on a city map, a starting point and a destination.

Suppose there are two full bowls of cookies.

* 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 that exactly two of U, V, W are 0.

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 u ( x ) and v ( x ) are two continuously differentiable functions.

Suppose that X and Y are two plane projective curves defined over a field F that do not have a common component ( this condition is true if both X and Y are defined by different irreducible polynomials, in particular, it holds for a pair of " generic " curves ).

: Suppose that a falling body broke into two pieces.

Suppose I tie the two pieces together.

Suppose two black holes have the same masses, electrical charges, and angular momenta, but the first black hole is made out of ordinary matter whereas the second is made out of antimatter ; nevertheless, they will be completely indistinguishable to an observer outside the event horizon.

Between lines 124 and 125, Henry states " Ah Plantagenet, why seekest thou to depose me ?/ Are we not both Plantagenets by birth ?/ And from two brothers lineally descent ?/ Suppose by right and equity thou be king ...".

Suppose that M is a smooth manifold containing a point p. We shall define the jets of curves through p, by which we henceforth mean smooth functions such that f ( 0 )= p.

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

Suppose γ is a path from x to y in M. The above equation defining parallel sections is a first-order ordinary differential equation ( cf.

Suppose that the curve γ is parameterized with respect to its arclength s. Then the arclength along the evolute E from s < sub > 1 </ sub > to s < sub > 2 </ sub > is given by

Suppose that γ is a G-valued field on the complex plane.

) 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 that u and v satisfy the Cauchy – Riemann equations in an open subset of R < sup > 2 </ sup >, and consider the vector field

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

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

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

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 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 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.

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 an array A with elements indexed 1 to n is to be searched for a value x.

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

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: