Let P be the root of the unbalanced subtree, with R and L denoting the right and left children of P respectively.

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.

Let L be a first-order language.

Let f, g belong to L < sup > 1 </ sup >( R < sup > n </ sup >).

Let L be an ordered set, called a concrete set and let L ′ be another ordered set, called an abstract set.

Let L < sub > 1 </ sub >, L < sub > 2 </ sub >, L ′< sub > 1 </ sub > and L ′< sub > 2 </ sub > be ordered sets.

Let us suppose that L is a complete lattice and let f be a monotonic function from L into L. Then, any x ′ such that f ′( x ′) ≤ x ′ is an abstraction of the least fixed-point of f, which exists, according to the Knaster – Tarski theorem.

Theorem: Let R be a Dedekind domain with fraction field K. Let L be a finite degree field extension of K and denote by S the integral closure of R in L. Then S is itself a Dedekind domain.

Let A be the set of all subfields of L that contain K, ordered by inclusion.

Let B be the set of subgroups of Gal ( L / K ), ordered by inclusion.

* " Don't Wake Me Up, Let Me Dream " w. L .. Wolfe Gilbert m. Mabel Wayne

Let us now consider a three-dimensional cubical box that has a side length L ( see infinite square well ).

: Let L be a complete lattice and let f: L → L be an order-preserving function.

Let us now regard D as a linear operator on the subspace V.

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

Let and be differentiable functions, and let D be the total derivative operator.

* Let D < sub > 1 </ sub > and D < sub > 2 </ sub > be directed sets.

Let C and D be categories.

Let C and D be categories.

Let a trapezoid have vertices A, B, C, and D in sequence and have parallel sides AB and CD.

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 U be a simple right R-module and write D

Let C be the category of vector spaces K-Vect over a field K and let D be the category of algebras K-Alg over K ( assumed to be unital and associative ).

Let X and Y be objects of a category D. The product of X and Y is an object X × Y together with two morphisms

Let U be a functor from D to C, and let X be an object of C. Then the following statements are equivalent:

Let A, B, C and D be the hexes that make up a rhombus, with A and C being the non-touching pair.

Let P < sup >− 1 </ sup > DP be an eigendecomposition of M, where P is a unitary complex matrix whose rows comprise an orthonormal basis of eigenvectors of M, and D is a real diagonal matrix whose main diagonal contains the corresponding eigenvalues.

Let G be a k-regular graph with diameter D and eigenvalues of adjacency matrix.

* Baby D, singer (" Let me be your fantasy ") lived in Kingsbury.

Let it be D < sub > n </ sub >.

* Weir, D., Noyes, D. Raising Hell How the Center for Investigative Reporting Gets the Story, ( Chapter on " Let Them Eat est.

After the celebratory tone of Christ's reception into heaven, marked by the choir's D major acclamation " Let all the angels of God worship him ", the " Whitsun " section proceeds through a series of contrasting moods — serene and pastoral in " How beautiful are the feet ", theatrically operatic in " Why do the nations so furiously rage "— towards the Part II culmination of " Hallelujah ".

Let D, E and F be given on the lines BC, AC and AB so that the equation holds.

The first was " I Won't Let You Down " ( 1982 ), as the lead singer in the trio Ph. D., with Tony Hymas and Simon Phillips.

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??