Suppose G is an ordered abelian group, meaning an abelian group with a total ordering "<" respecting the group's addition, so that a < b if and only if a + c < b + c for all c. Let I be a well-ordered subset of G, meaning I contains no infinite descending chain.

Suppose, in addition, that the operations of integration and differentiation can be swapped for the second derivative of as well, i. e.,

Suppose there is a network of highways and transit systems and a proposed addition.

Suppose in addition that ρ ( A ) =

and I asked myself a question: Suppose I had the same number of peas as there are atoms in my body, how large an area would they cover??

Suppose there is a program

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

Suppose there was such a catalyst that shifted an equilibrium.

Suppose there is a fixed parameter that needs to be estimated.

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

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

* Suppose that there is a compression algorithm that transforms every file into a distinct file which is no longer than the original file, and that at least one file will be compressed into something that is shorter than itself.

Suppose that the set of indices such that is decidable ; then, there exists a function that returns if, and otherwise.

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 there are p pharisees.

Suppose that in a company there are the following staff:

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:

Suppose a particle starts at point A, and there is a force F acting on it.

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

Suppose there are two full bowls of cookies.

Suppose that x and y are real numbers and that y is a function of x, that is, for every value of x, there is a corresponding value of y.

Suppose P is a definable binary relation ( which may be a proper class ) such that for every set x there is a unique set y such that P ( x, y ) holds.

: Suppose there are three cottages on a plane ( or sphere ) and each needs to be connected to the gas, water, and electric companies.

Suppose that C is a twice continuously differentiable immersed plane curve, which here means that there exists parametric representation of C by a pair of functions such that the first and second derivatives of x and y both exist and are continuous, and

Suppose that in a month there are 12 articles of interest in those journals.

Suppose there is an engine violating the Kelvin statement: i. e., one that drains heat and converts it completely into work in a cyclic fashion without any other result.

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.

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.