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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 ⊗< sub > R </ sub > C and let g denote the induced bilinear form on V ⊗< sub > R </ sub > C. Let W be a maximal isotropic subspace, i. e. a maximal subspace of V such that g |< sub > W </ sub > = 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 < sub > e </ sub > Earth's angular velocity and ω < sub > p </ sub > the planet's angular velocity.

Let T < sub > ij </ sub > := e < sub > ij </ sub >( 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 ℓ ( e ) be the length of the edge e and θ ( e ) be the dihedral angle between the two faces meeting at e, measured in radians.

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 < sub > B </ sub >( 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 <

Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

Let denote the Bézier curve determined by the points P < sub > 0 </ sub >, P < sub > 1 </ sub >, ..., P < sub > n </ sub >.

Let P < sub > F </ sub > be the domain of a prefix-free universal computable function F. The constant Ω < sub > F </ sub > is then defined as

Let M be a smooth manifold and let x be a point in M. Let T < sub > x </ sub > M be the tangent space at x.

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

Let M be a smooth manifold and let f ∈ C ∞( M ) be a smooth function.

Let us for simplicity take, then < math > 0 < c =- 2a </ math > and.

Let and i

Let X be some repeatable process, and i be some point in time after the start of that process.

Let x, y, z be a system of Cartesian coordinates in 3-dimensional Euclidean space, and let i, j, k be the corresponding basis of unit vectors.

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

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

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 I consist of three elements i, j, and k with i ≤ j and i ≤ k ( not directed ).

Let the mutation rate correspond to the probability that a j type parent will produce an i type organism.

Let J be a directed poset ( considered as a small category by adding arrows i → j if and only if i ≤ j ) and let F: J op → C be a diagram.

Let ( S, f ) be a game with n players, where S < sub > i </ sub > is the strategy set for player i, S = S < sub > 1 </ sub > × S < sub > 2 </ sub > ... × S < sub > n </ sub > is the set of strategy profiles and f =( f < sub > 1 </ sub >( x ), ..., f < sub > n </ sub >( x )) is the payoff function for x S. Let x < sub > i </ sub > be a strategy profile of player i and x < sub >- i </ sub > be a strategy profile of all players except for player i. When each player i < nowiki >

Let and </

Genesis 1: 9 " And God said, Let the waters be collected ". Letters in black, niqqud in red , cantillation in blue

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

Let and denote

Let Af denote the form of Af.

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 < sub > x </ sub >, defined by

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 < sub > 2 </ sub >( 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.

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