Let us for simplicity take m = k as an example.

Let x, y, z be a system of Cartesian coordinates in 3-dimensional Euclidean space, and let i, j, k be the corresponding basis of unit vectors.

Let k be an integer, and consider the integral

Let k be an integer that counts the steps of the algorithm, starting with zero.

Let k >= 1.

Let φ be a formula of degree k + 1 ; then we can write it as

* Let I consist of three elements i, j, and k with i ≤ j and i ≤ k ( not directed ).

Proof: Let d be the position of the leftmost ( most significant ) nonzero bit in the binary representation of s, and choose k such that the dth bit of x < sub > k </ sub > is also nonzero.

Let ω be a generator of W ′< sup > k </ sup >.

Let k be a field ( such as the rational numbers ) and K be an algebraically closed field extension ( such as the complex numbers ), consider the polynomial ring kX < sub > n </ sub > and let I be an ideal in this ring.

Let z be a primitive nth root of unity and let k be a positive integer.

Let V be a vector space over a field k. The core of the contraction operation, and the simplest case, is the natural pairing of V with its dual vector space V *.

Let n = 2 < sup > k </ sup >+ b, for 0 ≤ b ≤ 2 < sup > k </ sup >.

Let Z be a complex submanifold of X of dimension k, and let i: Z → X be the inclusion map.

Let k be an algebraically closed field and let A < sup > n </ sup > be an affine n-space over k. The polynomials ƒ in the ring k ..., x < sub > n </ sub > can be viewed as k-valued functions on A < sup > n </ sup > by evaluating ƒ at the points in A < sup > n </ sup >, i. e. by choosing values in k for each x < sub > i </ sub >.

Let k be an algebraically closed field and let P < sup > n </ sup > be a projective n-space over k. Let f ∈ k ..., x < sub > n </ sub > be a homogeneous polynomial of degree d. It is not well-defined to evaluate f on points in P < sup > n </ sup > in homogeneous coordinates.

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 us suppose that the animal did not in fact fall into the trap and did not suffer at all, but that we mistakenly believe it did, and say as before that its suffering was an evil thing.

Let us suppose ( as is the practical case ) that the star is sufficiently distant that all light from the star travels in parallel paths to the Earth observer, regardless of where the Earth is in its orbit.

The Beatles ' 1968 track " Back in the U. S. S. R " references the instrument in its final verse (" Let me hear your balalaikas ringing out / Come and keep your comrade warm ").

Let it go beyond a certain point, and it will tend for a time to gain strength from its own development as its effects spread and return to intensify the process of collapse ”.

( Let The Music Play )" can be considered part of the freestyle genre due to its use of a sample from the song, " Let The Music Play ", by Shannon.

“ Let the Music Play ”, by Shannon, is often named as the genre's first hit, and its sound, called " The Shannon Sound ," as the foundation of the genre.

After telling the audience " I shall now read to you the scroll of the Establishment of the State, which has passed its first reading by the National Council ", Ben-Gurion proceeded to read out the declaration, taking 16 minutes, ending with the words " Let us accept the Foundation Scroll of the Jewish State by rising " and calling on Rabbi Fishman to recite the Shehecheyanu blessing.

Before he died, Rabbeinu HaKadosh said: ‘ I need my sons !… Let the lamp continue to burn in its usual place ; let the table be set in its usual place ; let the bed be made in its usual place .” ( Kesubbos / Ketubot 103a )

Let w < sub > j </ sub > be the ' price ' ( the rental ) of a certain factor j, let MP < sub > j1 </ sub > and MP < sub > j2 </ sub > be its marginal product in the production of goods 1 and 2, and let p < sub > 1 </ sub > and p < sub > 2 </ sub > be these goods ' prices.

Let a light beam travel down the vertical line TP and bounce off from P. The beam's angle of inclination from the mirror is, so when it bounces off, its angle of inclination must be equal to.

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.

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

If V is a real vector space, then we replace V by its complexification V ⊗< sub > R </ sub > C and let g denote the induced bilinear form on V ⊗< sub > R </ sub > C. Let W be a maximal isotropic subspace, i. e. a maximal subspace of V such that g |< sub > W </ sub > = 0.

Let X be some set, and 2 < sup > X </ sup > symbolically represent its power set.

The film and its successors spawned countless imitators that borrowed elements instituted by Romero: Tombs of the Blind Dead, Let Sleeping Corpses Lie ( film ), Zombi 2, Hell of the Living Dead, Night of the Comet, Return of the Living Dead, Night of the Creeps, Children of the Living Dead, and the video game series Resident Evil ( later adapted as films in 2002, 2004, 2007 and 2010 ), Dead Rising, and House of the Dead.

There is also a quote etched in the marble of the chamber, as stated by venerable statesman Daniel Webster: " Let us develop the resources of our land, call forth its powers, build up its institutions, promote all its great interests, and see whether we also, in our day and generation, may not perform something worthy to be remembered.

Let the Government labour to its utmost, let the Legislature labour days and nights in your service ; but, after the very best has been attained and achieved, the question whether the English father is to be the father of a happy family and the centre of a united home is a question which must depend mainly upon himself.