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 G and H are topologically finitely-generated profinite groups which are isomorphic as discrete groups by an isomorphism ι.

Proof: Suppose G = ⟨ H | R ⟩ is a finitely presented, residually finite group.

Remark: Suppose G

Suppose G is a group.

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 we have a connected graph G = ( V, E ), The following statements are equivalent:

'" G. K. Chesterton suggested that Dickens " may never once have had the unfriendly thought, ' Suppose Hunt behaved like a rascal!

Suppose that the linear differential operator L is the Laplacian,, and that there is a Green's function G for the Laplacian.

Suppose G and H are given as before, along with group homomorphisms

Let π: E → X be a fibre bundle over a topological space X with structure group G and typical fibre F. By definition, there is a left action of G ( as a transformation group ) on the fibre F. Suppose furthermore that this action is effective.

Suppose that M is a Cartan geometry modelled on G / H, and let ( Q, α ) be the principal G-bundle with connection, and ( P, η ) the corresponding reduction to H with η equal to the pullback of α.

The covariant derivative can also be constructed from the Cartan connection η on P. In fact, constructing it in this way is slightly more general in that V need not be a fully fledged representation of G. Suppose instead that that V is a (, H )- module: a representation of the group H with a compatible representation of the Lie algebra.

Suppose that V is only a representation of the subgroup H and not necessarily the larger group G. Let be the space of V-valued differential k-forms on P. In the presence of a Cartan connection, there is a canonical isomorphism

Suppose that G is a group and K is a field.

Suppose G is a finitely generated group ; and T is a finite symmetric set of generators

Suppose a group G acts upon A, and that H is a unitary representation of both A and G which is equivariant in the sense that for all g in G, a in A and ψ in H,

Suppose that O is an invariant subalgebra of A under G ( all observables are invariant under G, but not every self-adjoint operator invariant under G is necessarily an observable ).

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

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.

Suppose C is the complexity class of problems solvable in logarithmithic space with probabilistic Turing machines that never accept incorrectly but are allowed to reject incorrectly less than 1 / 3 of the time ; this is called one-sided error.

Suppose that is a code word with fewer than non-zero terms.

Suppose the typewriter has 50 keys, and the word to be typed is banana.

Suppose, dear sir, someone actually took our word for it?

Suppose a reader comes across an unknown word such as despisement meaning " an attitude of despising ".

Suppose Bob and Alice start with a document containing the word Mary.