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Let and denote

Let Af denote the form of Af.

Let denote the Bézier curve determined by the points P 0 , P 1 , ..., P n .

Let X denote a Cauchy distributed random variable.

Let w denote the weight per unit length of the chain, then the weight of the chain has magnitude

Let denote the equivalence class to which a belongs.

Let '~' denote an equivalence relation over some nonempty set A, called the universe or underlying set.

Let G denote the set of bijective functions over A that preserve the partition structure of A: ∀ x ∈ A ∀ g ∈ G ( g ( x ) ∈ ).

Let G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.

Let R denote the field of real numbers.

Let n denote a complete set of ( discrete ) quantum numbers for specifying single-particle states ( for example, for the particle in a box problem we can take n to be the quantized wave vector of the wavefunction.

Let ε ( n ) denote the energy of a particle in state n. As the particles do not interact, the total energy of the system is the sum of the single-particle energies.

Let denote the space of scoring functions.

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 us denote the time at which it is decided that the compromise occurred as T.

Let denote the sequence of convergents to the continued fraction for.

Let us denote the mutually orthogonal single-particle states by and so on.

That is, Alice has one half, a, and Bob has the other half, b. Let c denote the qubit Alice wishes to transmit to Bob.

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 x , defined by

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

Let Q ( x ) denote the number of square-free ( quadratfrei ) integers between 1 and x.

A possible definition of spoiling based on vote splitting is as follows: Let W denote the candidate who wins the election, and let X and S denote two other candidates.

Let π 2 ( x ) denote the number of primes p ≤ x such that p + 2 is also prime.

Let be a sequence of independent and identically distributed variables with distribution function F and let denote the maximum.

Let and set

Let me set the record this time, and let me get back OK, so the German will give me the exclusive.

Let him bounce back, and he could really set up the staff.

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 Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )

Let A be a set, and apply the axiom of regularity to

Most recently Chuck D became involved in Let Freedom Sing: The Music of the Civil Rights, a 3-CD box set from Time Life.

He's also set to appear in a follow up movie called Let Freedom Sing: The Music That Inspired the Civil Rights Movement.

* Let X be a simply ordered set endowed with the order topology.

Let M be a smooth manifold and let x be a point in M. Let I x be the ideal of all functions in C ∞( M ) vanishing at x, and let I x 2 be the set of functions of the form, where f i , g i ∈ I x .

Let X be a nonempty set, and let.

Let X be a finite set with n elements.

* Let be the set of ordered pairs of integers with not zero, and define an equivalence relation on according to which if and only if.

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

The 2005 Kazuo Ishiguro novel Never Let Me Go and the 2010 film adaption are set in an alternate history in which cloned humans are created for the sole purpose of providing organ donations to naturally born humans.

Let ƒ be a function whose domain is the set X, and whose range is the set Y.

Let ( S ,*) be a set S with a binary operation * on it ( known as a magma ).

* Let the index set I of an inverse system ( X i , f ij ) have a greatest element m. Then the natural projection π m : X → X m is an isomorphism.

Let and all

Let all projects dry slowly for several days.

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 us also assume the existence of only one class or type of service, all of which is supplied at the same voltage, phase, etc. to residential, commercial, and industrial customers.

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 Af where the maximization is over all admissible policies Af.

Let them be candidly reviewed under a sense of the difficulty of combining in one system the various sentiments and interests of a continent divided into so many sovereign and independent communities, under a conviction of the absolute necessity of uniting all our councils and all our strength, to maintain and defend our common liberties ...

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.

:: Let no-one deceive you by any means, for that day will not come unless the falling away comes first, and the man of sin is revealed, the son of perdition, who opposes and exalts himself above all that is called God or that is worshiped, so that he sits as God in the temple of God, showing himself that he is God. Thess 2: 3-4

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.

Col 3: 16 " Let the word of Christ dwell in you believers richly, teaching and admonishing one another in all wisdom, singing psalms and hymns and spiritual songs, with thankfulness in your hearts to God.

Let us call the class of all such formulas R. We are faced with proving that every formula in R is either refutable or satisfiable.

: Let all behold and glorify Jesus Christ,

Let us face reality that " all businesses recover ", whether they planned for recovery or not, simply because business is about earning money for survival.

Let ( I, ≤) be a directed poset ( not all authors require I to be directed ).

Let ( A i ) i ∈ I be a family of groups and suppose we have a family of homomorphisms f ij : A j → A i for all i ≤ j ( note the order ) with the following properties:

Indeed, the great mercy of God who desires that all men should be saved, and Jesus ' tenderness toward children which caused him to say: ' Let the children come to me, do not hinder them ,' allow us to hope that there is a way of salvation for children who have died without Baptism.

Psalms 33: 8-9: Let all the earth fear the LORD: let all the inhabitants of the world stand in awe of him.

Let therefore hatred depart from among you, let your quarrels end, let wars cease, and let all dissensions and controversies slumber.

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