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Page "Hilbert's third problem" ¶ 17

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Let and ℓ

Let H = ℓ 2 ( N ) and consider the sequence

Let S be the shift operator on the sequence space ℓ ∞( Z ), which is defined by ( Sx ) i = x i + 1 for all x ∈ ℓ ∞( Z ), and let u ∈ ℓ ∞( Z ) be the constant sequence u i = 1 for all i ∈ Z.

Let p be a point of P 2 and ℓ a line of the dual projective plane.

Let < var > C </ var > be the foot of the perpendicular from < var > B </ var > to ℓ 2 .

Let and e

* 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 e be the error in b. Assuming that A is a square matrix, the error in the solution A − 1 b is A − 1 e.

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 be a set with a binary operation ( i. e., a magma ).

Let T: X → X be a contraction mapping on X, i. e.: there is a nonnegative real number q < 1 such that

Let G be a group with identity element e, N a normal subgroup of G ( i. e., N ◁ G ) and H a subgroup of G. The following statements are equivalent:

Let A be an m by n matrix ( i. e., A has m rows and n columns ).

Let us consider two patterns made of parallel and equidistant lines, e. g., vertical lines.

Let be an interval of real numbers ( i. e. a non-empty connected subset of ).

Let K be a number field ( i. e., a finite extension of ), in other words, for some by the primitive element theorem.

Let T be the period ( for example the time between two greatest eastern elongations ), ω be the relative angular velocity, ω e Earth's angular velocity and ω p the planet's angular velocity.

Let T ij := e ij ( 1 ) be the elementary matrix with 1's on the diagonal and in the ij position, and 0's elsewhere ( and i ≠ j ).

and switches between b-1 and b bits for Golomb code ( i. e. M is not a power of 2 ): Let.

Let e be an index of the composition, which is a total computable function.

Let M be a monoid with identity element e and let A be the set of all subsets of M. For two such subsets S and T, let S + T be the union of S and T and set ST =

Both Kember and Pierce continue to perform some Spacemen 3 songs live ( e. g. " Transparent Radiation ", " Revolution ", " Suicide ", " Set Me Free ", " Che " and " Let Me Down Gently " ; and " Walkin ' with Jesus ", " Amen " and " Lord Can You Hear Me?

Many episode titles parodied the titles of Bond films, e. g. “ Live and Let ’ s Dance .”

Let K be a field, and let A be a vector space over K equipped with an additional binary operation from A × A to A, denoted here by · ( i. e. if x and y are any two elements of A, x · y is the product of x and y ).

Let B be a complex Banach algebra containing a unit e. Then we define the spectrum σ ( x ) ( or more explicitly σ B ( x )) of an element x of B to be the set of those complex numbers λ for which λe − x is not invertible in B.

Let and be

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??

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