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

Suppose that X and Y are a pair of commuting vector fields.

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 F is a collection of continuous linear operators from X to Y.

Suppose C is a category, and f: X → Y is a morphism in C. The morphism f is called a constant morphism ( or sometimes left zero morphism ) if for any object W in C and any g, h: W → X, fg

Suppose the random column vectors X, Y live in R < sup > n </ sup > and R < sup > m </ sup > respectively, and the vector ( X, Y ) in R < sup > n + m </ sup > has a multivariate normal distribution whose variance is the symmetric positive-definite matrix

* Suppose that f is flat and that F is a quasi-coherent module over Y.

Suppose that X, Y, and Z as above are sets, and that f: Z → X and g: Z → Y are set functions.

# Suppose φ: X → Y is a morphism of schemes of locally finite type over C. Then there exists a continuous map φ < sup > an </ sup >: X < sup > an </ sup > → Y < sup > an </ sup > such λ < sub > Y </ sub > ° φ < sup > an </ sup >

Suppose the spaces X and Y are topological spaces, endowed with the topology O ( X ) and O ( Y ) of open sets on X and Y.

Suppose a firm's output Y is given by the production function where K and L are inputs to production ( say, capital and labor ).

Suppose X and Y are two independent tosses of a fair coin, where we designate 1 for heads and 0 for tails.

Suppose response variable Y is binary, that is it can have only two possible outcomes which we will denote as 1 and 0.

Suppose we have morphisms from X to Y and Y to Z, so that we also have a composed morphism from X to Z.

Suppose two random variables X and Y are jointly normally distributed.

Suppose Af is defined in the sub-interval Af.

Suppose they both had ventured into realms which their colleagues thought infidel: is this the way gentlemen settle frank differences of opinion??

Suppose, says Dr. Lyttleton, the proton has a slightly greater charge than the electron ( so slight it is presently immeasurable ).

Suppose it is something right on the planet, native to it.

Suppose there is a program

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

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

Alex is the majority shareholder, and Betty is the minority shareholder. Suppose now that Worldwide is the chain being acquired.

Suppose that R ( x, y ) is a relation in the xy 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 a car is driving up a tall mountain.

Suppose that the car is ascending at 2. 5 km / h.

Suppose the vector field describes the velocity field of a fluid flow ( such as a large tank of liquid or gas ) and a small ball is located within the fluid or gas ( the centre of the ball being fixed at a certain point ).

Suppose that F is a partial function that takes one argument, a finite binary string, and possibly returns a single binary string as output.

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.

; 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 is a complex-valued function which is differentiable as a function.

Suppose a mass is attached to a spring which exerts an attractive force on the mass proportional to the extension / compression of the spring.

Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.

Suppose that the distribution consists of a number of discrete probability masses p < sub > k </ sub >( θ ) and a density f ( x | θ ), where the sum of all the ps added to the integral of f is always one.

Suppose v < sub > 1 </ sub > and v < sub > 2 </ sub > are known pseudovectors, and v < sub > 3 </ sub > is defined to be their sum, v < sub > 3 </ sub >= v < sub > 1 </ sub >+ v < sub > 2 </ sub >.

Suppose we are using six-digit decimal floating point arithmetic, sum has attained the value 10000. 0, and the next two values of input ( i ) are 3. 14159 and 2. 71828.

Suppose that one is summing n values x < sub > i </ sub >, for i = 1 ,..., n. The exact sum is:

Suppose that the sum of the two input signals is applied to a diode, and that an output voltage is generated that is proportional to the current through the diode ( perhaps by providing the voltage that is present across a resistor in series with the diode ).

Suppose − 1 is not a sum of squares, then a Zorn's Lemma argument shows that the prepositive cone of sums of squares can be extended to a positive cone P ⊂ F.

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 now that, more generally, a rearranged series of the alternating harmonic series is organized in such a way that the ratio between the number of positive and negative terms in the partial sum of order n tends to a positive limit r. Then, the sum of such a rearrangement will be

Take, in order, just enough positive terms so that their sum exceeds M. Suppose we require p terms – then the following statement is true: