Let φ be a net on X based on the directed set D and let A be a subset of X, then φ is said to be frequently in ( or cofinally in ) A if for every α in D there exists some β ≥ α, β in D, so that φ ( β ) is in A.

Let α = BAO and β = OBC.

Let α and β be two differential forms on M, and let X and Y be two vector fields.

Let α be the next n digits of the radicand, and β be the next digit of the root.

Let φ be the sentence β (< u >#( β )</ u >).

Let α be the phase of the first input and β be the phase of the second.

Let f < sub > 1 </ sub >: ( X < sub > 1 </ sub >, α < sub > 1 </ sub >) → ( Y < sub > 1 </ sub >, β < sub > 1 </ sub >) and f < sub > 2 </ sub >: ( X < sub > 2 </ sub >, α < sub > 2 </ sub >) → ( Y < sub > 2 </ sub >, β < sub > 2 </ sub >) be morphisms of motives.

Let the variance-covariance matrix for the observations be denoted by M and that of the parameters by M < sup > β </ sup >.

Let GF ( p < sup > m </ sup >) be a field with p < sup > m </ sup > elements, and β an element of it such that the m elements

Let a rigid object move along a regular curve described parametrically by β ( t ).

Let α and β be partial transformations of a set

Let the acute angle between X and Y be α, Y and Z be β.

Let the open enemy to it be regarded as a Pandora with her box opened ; ;

Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.

`` Let him be now ''!!

Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

Let Af be the null space of Af.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.

Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.

Let this be denoted by Af.

Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.

Let not your heart be troubled, neither let it be afraid ''.

The same God who called this world into being when He said: `` Let there be light ''!!

For those who put their trust in Him He still says every day again: `` Let there be light ''!!

Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.

Let her out, let her out -- that would be the solution, wouldn't it??

Let P < sub > F </ sub > be the domain of a prefix-free universal computable function F. The constant Ω < sub > F </ sub > is then defined as

Let indicate the circumference of a circle of radius in a space of constant curvature.

Let x be a spatial coordinate, and let the direction of the constant acceleration as well as the spaceship's velocity ( relative to the rest frame ) be parallel to the x-axis.

Let be the set of non-negative integers ( natural numbers ), let n be any fixed constant, and let be the set of-tuples of natural numbers.

Let be in motion relative to with constant velocity ; without loss of generality, we will take this motion to be directed only along the x-axis.

Let M be the total mass, which is constant, so the left side can be multiplied and divided by M, so

Let be a new unknown constant,, so

Let U be an open set in a manifold M, Ω < sup > 1 </ sup >( U ) be the space of smooth, differentiable 1-forms on U, and F be a submodule of Ω < sup > 1 </ sup >( U ) of rank r, the rank being constant in value over U. The Frobenius theorem states that F is integrable if and only if for every the stalk F < sub > p </ sub > is generated by r exact differential forms.

Let S be the shift operator on the sequence space ℓ < sup >∞</ sup >( Z ), which is defined by ( Sx )< sub > i </ sub > = x < sub > i + 1 </ sub > for all x ∈ ℓ < sup >∞</ sup >( Z ), and let u ∈ ℓ < sup >∞</ sup >( Z ) be the constant sequence u < sub > i </ sub > = 1 for all i ∈ Z.

* Let be the locally constant sheaf.

* Let be the sheaf of holomorphic functions on the compact connected complex manifold X, then by the maximum principle, global sections are constant, ie.

Let be the uniform distance between the function and the set of all Lipschitz real-valued functions on having Lipschitz constant:

Let z = ( 0y )< sup > k </ sup >, which can be computed in constant time ( multiply y by the constant ( 0 < sup > b </ sup > 1 )< sup > k </ sup >).

Let be a holomorphic function on the open ball centered at zero and radius in the complex plane, and assume that is not a constant function.

Let a first-order language be given, with the the set of constant symbols, the set of ( individual ) variables, the set of functional operators, and the set of predicate symbols.

Let q < sub > 1 </ sub > and q < sub > 2 </ sub > be two fixed points in the plane and let b be a constant.

* Let be a constant, and.