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 P ( α ) be a property defined for all ordinals α.

The All Things Must Pass track " Ballad of Sir Frankie Crisp ( Let It Roll )" was inspired by Friar Park's history, and the lyrics of later songs such as " Ding Dong, Ding Dong " and " The Answer's at the End " directly quote from the many carvings around the property.

Let p: E → B be a basepoint-preserving Serre fibration with fiber F, that is, a map possessing the homotopy lifting property with respect to CW complexes.

: Let be a property provable about objects of type.

Let X be any Lie algebra over K. Given a unital associative K-algebra U and a Lie algebra homomorphism: h: X → U < sub > L </ sub >, ( notation as above ) we say that U is the universal enveloping algebra of X if it satisfies the following universal property: for any unital associative K-algebra A and Lie algebra homomorphism f: X → A < sub > L </ sub > there exists a unique unital algebra homomorphism g: U → A such that: f (-) = g < sub > L </ sub > ( h (-)).

Let X be a compact Hausdorff space that satisfies the property that no one-point set is open.

Let K < sub > X </ sub >< sup > pre </ sup > be the presheaf whose sections on U are localizations S < sub > U </ sub >< sup >- 1 </ sup > Γ ( U, O < sub > X </ sub >) and whose restriction maps are induced from the restriction maps of O < sub > X </ sub > by the universal property of localization.

Let us attempt to find a solution which is not identically zero satisfying the boundary conditions but with the following property: u is a product in which the dependence of u on x, t is separated, that is:

Let Q be such a property.

Let denote the complement of L. By the definition of PP there is a polynomial-time probabilistic algorithm A with the property that and.

Let no man insult the metropolitan church of which Peter is head, or his service or his churchman ; let no man seize their property, goods or people, let no man meddle in the affairs of the church ... Their laws, their churches and monasteries and chapels shall be respected ; whoever condemns or blames this religion, shall not be allowed to excuse himself under any pretext, but shall be punished with death.

Let us define the covariance matrix of the noise, reminding ourselves that this matrix has Hermitian symmetry, a property that will become useful in the derivation:

Let it simply be asked: Where is the security for property, for reputation, for life, if the sense of religious obligation desert the oaths which are the instruments of investigation in courts of justice?

Let X be a finite subset of U, minimal with respect to the property that it generates U. Since U is non-zero, this set X is nonempty.

Let φ: S → 2 < sup > S </ sup > be a set-valued function on S with a closed graph and the property that φ ( x ) is non-empty and convex for all x ∈ S. Then φ has a fixed point.

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 T be a linear operator represented by the matrix

Let the samples of be represented by the sequence, and let be represented by the sequence which correspond to the same points in time.

Let the samples of be represented by the sequence, and let be represented by the sequence which correspond to the same points in time.

Let the coin tosses be represented by a sequence of independent random variables, each of which is equal to H with probability p, and T with probability Let N be time of appearance of the first H ; in other words,, and If the coin never shows H, we write N is itself a random variable because it depends on the random outcomes of the coin tosses.

Let open be chosen from a set of size, i. e., it can represented as a k bit string, and let be the corresponding commitment scheme.

* Let, where || denotes concatenation and is represented as a bit string.

Lindsay's vision was represented on songs such as " Let Me " ( a 1969 gold single ), and the albums Hard ' N ' Heavy ( with marshmallow ) and Alias Pink Puzz.

Let these rotations and reflections operate on all points on the plane, and let these points be represented by position vectors.

Let the available colors be represented by the q < sup > 2 </ sup > different two-digit numbers in radix q.

Thus Q defines an inner product on dom T. Let H < sub > 1 </ sub > be the completion of dom T with respect to Q. H < sub > 1 </ sub > is an abstractly defined space ; for instance its elements can be represented as equivalence classes of Cauchy sequences of elements of dom T. It is not obvious that all elements in H < sub > 1 </ sub > can identified with elements of H. However, the following can be proved:

Anghel, along with the percussion band Sistem, represented Romania at the Eurovision Song Contest 2005, with the song Let Me Try, where they were ranked third in the final, Romania's best ever result at Eurovision.

Let the edges be coloured red or blue depending on whether the two people represented by the vertices connected by the edge are mutual strangers or mutual acquaintances, respectively.