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 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 H be a Hilbert space, and let H * denote its dual space, consisting of all continuous linear functionals from H into the field R or C. If x is an element of H, then the function φ < sub > x </ sub >, defined by

Let be the space of real-valued continuous functions on X which vanish at infinity ; that is, a continuous function f is in if, for every, there exists a compact set such that on

Let K be a topological field, namely a field with a topology such that addition, multiplication, and division are continuous.

Let X be a topological vector space over K. Namely, X is a K vector space equipped with a topology so that vector addition and scalar multiplication are continuous.

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 Met < sub > c </ sub > be the category of metric spaces with continuous functions for morphisms.

Let X be a random variable with a continuous probability distribution with density function f depending on a parameter θ.

Let K be the set C of all complex numbers, and let V be the set C < sub > C </ sub >( R ) of all continuous functions from the real line R to the complex plane C.

* The ring of continuous functions from the real numbers to the real numbers is not Noetherian: Let I < sub > n </ sub > be the ideal of all continuous functions f such that f ( x ) = 0 for all x ≥ n. The sequence of ideals I < sub > 0 </ sub >, I < sub > 1 </ sub >, I < sub > 2 </ sub >, etc., is an ascending chain that does not terminate.

Let C ( R ) be the subset consisting of continuous functions.

Let denote the number of kernels which have popped up to time t. Then this is a continuous time, non-homogenous Markov process.

Let ƒ and g be two functions satisfying the above hypothesis that ƒ is continuous on I and is continuous on the closed interval.

Let U be an open set in R < sup > n </ sup > and φ: U → R < sup > n </ sup > an injective differentiable function with continuous partial derivatives, the Jacobian of which is nonzero for every x in U. Then for any real-valued, compactly supported, continuous function f, with support contained in φ ( U ),

Let φ: X → Y be a continuous and absolutely continuous function ( where the latter means that ρ ( φ ( E )) = 0 whenever μ ( E ) = 0 ).

Let C be a positively oriented, piecewise smooth, simple closed curve in the plane < sup > 2 </ sup >, and let D be the region bounded by C. If L and M are functions of ( x, y ) defined on an open region containing D and have continuous partial derivatives there, then

Let f: Y → X be a continuous map.

Let u and v be continuous functions in x, and let dx, du and dv be infinitesimals within the framework of non-standard analysis, specifically the hyperreal numbers.

Let I be an interval in the real line R. A function f: I → R is absolutely continuous on I if for every positive number, there is a positive number such that whenever a finite sequence of pairwise disjoint sub-intervals ( x < sub > k </ sub >, y < sub > k </ sub >) of I satisfies