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 were a universal solvable word problem group.

Suppose G is a group.

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 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 a partially ordered set P has the property that every chain ( i. e. totally ordered subset ) has an upper bound in P. Then the set P contains at least one maximal element.

Suppose ( P ,≤) is a partially ordered set.

Suppose a non-empty partially ordered set P has the property that every non-empty chain has an upper bound in P. Then the set P contains at least one maximal element.

Suppose an ordered and complete single-particle basis

Suppose there are six cities, which we'll call A, B, C, D, E, and F. A good design for our chromosome might be the ordered list we want to try.

Suppose V is an infinite dimensional vector space over a field F. If the dimension is κ, then there is some basis of κ elements for V. After an order is chosen, the basis can be considered an ordered basis.