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 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 the lines in front of the movie houses were too long and we couldn't get in??

Suppose, he says, that the tables were turned, and we were in the Soviets' position: `` There would be more than 2,000 modern Soviet fighters, all better than ours, stationed at 250 bases in Mexico and the Caribbean.

Suppose that this one were to work??

Take as an example a program that looks up a specific entry in a sorted list of size n. Suppose this program were implemented on Computer A, a state-of-the-art machine, using a linear search algorithm, and on Computer B, a much slower machine, using a binary search algorithm.

Suppose per contra that were a non-finitely generated left-ideal.

Suppose someone buys all the planks, masts and whatever that is stored in the warehouse, and out of all of those materials, and absolutely no others, he builds a ship according to the same plans that were used to build the ship, christened " the Theseus ".

Suppose that the universe were not expanding, and always had the same stellar density ; then the temperature of the universe would continually increase as the stars put out more radiation.

:: “ 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 G were a universal solvable word problem group.

Suppose we were to increase the concentration of CO in the system.

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.

Mendelssohn answered in an open letter in December 1769: " Suppose there were living among my contemporaries a Confucius or a Solon, I could, according to the principles of my faith, love and admire the great man without falling into the ridiculous idea that I must convert a Solon or a Confucius.

Suppose the total composition were 50 / 50 %.

Suppose that we had a proof that all sets of four horses were the same color.

Suppose, however, that the course was pass / fail and students were required to score above 70 on both tests to pass.

Suppose a president were being elected among three candidates, a left, a right, and a center candidate, and 100 votes cast.

Suppose that supporters of the 2004 Republican candidate, George W. Bush, had set up vote pairing web sites so that Buchanan supporters from swing states in the US ( such as Ohio, where the Democrats and Republicans were in a close race ) would get matched with Bush supporters in solidly Democrat states ( such as Massachusetts ).

Suppose further that if the young man were to disappear, no one would suspect the doctor.

Suppose it is necessary to know the price of the oil at 12: 00PM on one particular day in the past ; one must base the estimate on any number of samples that were obtained on the days before and after the event.

Suppose Atwood were to fraudulently sell the same property to another person, Dunn.