Suppose v, e, and f are the number of vertices, edges, and regions.

Suppose that I is an interval b in the real numbers R and that f: I → R is a continuous function.

It is frequently stated in the following equivalent form: Suppose that is continuous and that u is a real number satisfying or Then for some c ∈ b, f ( c ) = u.

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 f were injective, which means the pieces of S cut out by the squares stack up in a non-overlapping way.

Suppose U is an open subset of the complex plane C, f: U → C is a holomorphic function and the closed disk

Suppose U is a simply connected open subset of the complex plane, and a < sub > 1 </ sub >,..., a < sub > n </ sub > are finitely many points of U and f is a function which is defined and holomorphic on U

Suppose f is an analytic function defined on an open subset U of the complex plane.

Suppose there is a sample of n independent and identically distributed observations, coming from a distribution with an unknown probability density function f < sub > 0 </ sub >(·).

Suppose that g and h are total computable functions that are used in a recursive definition for a function f:

where g ( w ) = f ( w ) v. Suppose that V is finite dimensional.

Suppose that one computes the MDCT of the subsequent, 50 % overlapped, 2N block ( c, d, e, f ).

Suppose that the programmable divider, using N, is only able to operate at a maximum clock frequency of 10 MHz, but the output f is in the hundreds of MHz range ;.

Suppose f ( x, y ) is A × B measurable.

Suppose that f ( p, q, t ) is a function on the manifold.

Suppose f is bounded: i. e. there exists a constant M such that | f ( z )| ≤ M for all z.

Suppose that f is entire and | f ( z )| is less than or equal to M | z |, for M a positive real number.

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

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 we define V to be the set of variables on which the functions f and g operate.

Suppose that f is a homomorphism between one dimensional formal group laws over a field of characteristic p > 0.

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 minimal polynomial for T decomposes over F into a product of linear polynomials.

Suppose a is a root of polynomial P, with multiplicity m > 1.

Suppose that the interpolation polynomial is in the form

Suppose we interpolate through n + 1 data points with an at-most n degree polynomial p ( x ) ( we need at least n + 1 datapoints or else the polynomial cannot be fully solved for ).

Suppose also another polynomial exists also of degree at most n that also interpolates the n + 1 points ; call it q ( x ).

Suppose we want to compute the characteristic polynomial of the matrix

Suppose we have the following polynomial with integer coefficients.

It is known that no non-constant polynomial function P ( n ) with integer coefficients exists that evaluates to a prime number for all integers n. The proof is: Suppose such a polynomial existed.

Suppose K is a Galois extension of the rational number field Q, and P ( t ) a monic integer polynomial such that K is a splitting field of P. It makes sense to factorise P modulo a prime number p. Its ' splitting type ' is the list of degrees of irreducible factors of P mod p, i. e. P factorizes in some fashion over the prime field F < sub > p </ sub >.