* Theorem Let X be a normed space.

* Corollary Let X be a reflexive normed space and Y a Banach space.

* Corollary Let X be a reflexive normed space.

Let X and Y be two K-vector spaces.

Let V, W and X be three vector spaces over the same base field F. A bilinear map is a function

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

Let X denote a Cauchy distributed random variable.

Let X be a nonempty set, and let.

: Theorem on projections: Let the function f: X → B be such that a ~ b → f ( a )

Let X be a finite set with n elements.

" Let X be the unit Cartesian square ×, and let ~ be the equivalence relation on X defined by ∀ a, b ∈ (( a, 0 ) ~ ( a, 1 ) ∧ ( 0, b ) ~ ( 1, b )).

Let X < sub > i </ sub > be the measured weight of the ith object, for i

Let X be a topological space, and let x < sub > 0 </ sub > be a point of X.

Let be the conditional probability distribution function of Y given X.

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

Let ( X < sub > i </ sub >, f < sub > ij </ sub >) be an inverse system of objects and morphisms in a category C ( same definition as above ).

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

Let there be a finite sequence of positive integers X

Let X be a measurable space, let μ be a measure on X, and let N be a measurable set in X.

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 now give some thought to the soul.

Let us now put some flesh on the theoretical bones we have assembled by giving illustrations of roleplaying used for evaluation and analysis.

Let A be a unital commutative Banach algebra over C. Since A is then a commutative ring with unit, every non-invertible element of A belongs to some maximal ideal of A.

Let S be a vector space over the real numbers, or, more generally, some ordered field.

Patrick described details of some of his abductions in his book Let Our Children Go!

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

Moving to groups in general, let H be a subgroup of some group G. Let ~ be an equivalence relation on G, such that a ~ b ↔ ( ab < sup >− 1 </ sup > ∈ H ).

Let Marcion then exhibit, as gifts of his god, some prophets, such as have not spoken by human sense, but with the Spirit of God, such as have both predicted things to come, and have made manifest the secrets of the heart ; let him produce a psalm, a vision, a prayer -- only let it be by the Spirit, in an ecstasy, that is, in a rapture, whenever an interpretation of tongues has occurred to him ; let him show to me also, that any woman of boastful tongue in his community has ever prophesied from amongst those specially holy sisters of his.

In his Commentary on Daniel, he noted, “ Let us not follow the opinion of some commentators and suppose him to be either the Devil or some demon, but rather, one of the human race, in whom Satan will wholly take up his residence in bodily form .” In interpreting 2 Thessalonians's claim that the Antichrist will sit in God's temple, Jerome preferred the view that the " temple " should be interpreted as the Church, not as the Temple in Jerusalem.

Let us briefly consider some of the arguments for and against the likelihood principle.

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

Let us therefore assume that this space without doubt belongs to the still undiscovered satellites of Mars, let us also add that perhaps Jupiter still has around itself some smaller ones which have not been sighted yet by any telescope.

According to some translations, the segment CE, representing the intelligible world, is divided into the same ratio as AC, giving the subdivisions CD and DE ( it can be readily verified that CD must have the same length as BC < ref > Let the length of AE be equal to and that of AC equal to, where < math >

" Let them produce the original records of their churches ; let them unfold the roll of their bishops, running down in due succession from the beginning in such a manner that first bishop of theirs bishop shall be able to show for his ordainer and predecessor some one of the apostles or of apostolic men, — a man, moreover, who continued steadfast with the apostles.

Let be a list of n linearly independent vectors of some complex vector space with an inner product.

Let f ( x ) and g ( x ) be two functions defined on some subset of the real numbers.

Let ( E < sub > n </ sub >) be a sequence of events in some probability space.

Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.

Let be a set of independent and identically distributed event observations, where all are distributed as for some.

Let us write the wave function of the universe as, where denotes the configuration variables associated to some subsystem ( I ) of the universe and denotes the remaining configuration variables.