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 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 V, W and X be three vector spaces over the same base field F. A bilinear map is a function

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 F be a prefix-free universal computable function.

Let E be the intersection of the diagonals, and let F be on side DA and G be on side BC such that FEG is parallel to AB and CD.

Let F be the continuous cumulative distribution function which is to be the null hypothesis.

Let F be a field.

Let the line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then ( 1 ) the distance from F to T is 2f, and ( 2 ) a tangent to the parabola at point T intersects the line of symmetry at a 45 ° angle.

These assumptions can be summarised as: Let ( Ω, F, P ) be a measure space with P ( Ω )= 1.

Let the input power to a device be a force F < sub > A </ sub > acting on a point that moves with velocity v < sub > A </ sub > and the output power be a force F < sub > B </ sub > acts on a point that moves with velocity v < sub > B </ sub >.

Let P be the following property of partial functions F of one argument: P ( F ) means that F is defined for the argument ' 1 '.

Let F and G be a pair of adjoint functors with unit η and co-unit ε ( see the article on adjoint functors for the definitions ).

Let X be a normed topological vector space over F, compatible with the absolute value in F. Then in X *, the topological dual space X of continuous F-valued linear functionals on X, all norm-closed balls are compact in the weak -* topology.

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 Af be the null space of Af.

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

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 be arbitrary elements of.

* Let be an arbitrary set, and let be the set of all bijective functions from to.

Let φ ( ξ, η, ζ ) be an arbitrary function of three independent variables, and let the spherical wave form F be a delta-function: that is, let F be a weak limit of continuous functions whose integral is unity, but whose support ( the region where the function is non-zero ) shrinks to the origin.

Let u, v be arbitrary vectors in a vector space V over F with an inner product, where F is the field of real or complex numbers.

Let N represent the common nine-point center and P be an arbitrary point in the plane of the orthocentric system.

Let us examine some other cases ; we shall find that Peacock's principle is not a solution of the difficulty ; the great logical process of generalization cannot be reduced to any such easy and arbitrary procedure.

Let us very roughly consider the line between the " leftmost " and " rightmost " two points of the k selected points ( for some arbitrary left / right axis: we can choose top and bottom for the exceptional vertical case ).

Let be an arbitrary topological space.

Let be an arbitrary real m-dimensional column vector of such that |||| = | α | for a scalar α.

Let ABC be an arbitrary triangle.

Let v be an arbitrary vector in V. There exist unique scalars such that:

: Let A and B be arbitrary formula of a formal language.

Let be an arbitrary field extension.

Let s be an arbitrary dimension and b < sub > 1 </ sub >, ..., b < sub > s </ sub > be arbitrary coprime integers greater than 1.

Let X be an arbitrary set and H a Hilbert space of complex-valued functions on X.

Let and be complex matrices and let and be arbitrary complex numbers.

Let be an arbitrary system subject to changes in time and let be an arbitrary event that is a stimulus for the system: we say that is an adaptive system if and only if when t tends to infinity the probability that the system change its behavior in a time step given the event is equal to the probability that the system change its behavior independently of the occurrence of the event.

* Let be an arbitrary finite set with at least two elements.

Let be an arbitrary qubit.

Let be the coordinate vector of an arbitrary point in the body with respect to the body-fixed frame.

Let σ be an arbitrary signature.

Let be a non-zero bit of arbitrary message,.