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Let K be the rational number field Q and
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Let and K
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 V and W be vector spaces over the same field K. A function f: V → W is said to be a linear map if for any two vectors x and y in V and any scalar α in K, the following two conditions are satisfied:
It was based on the Malayalam novel Nammukku Graamangalil Chennu Raappaarkkaam ( Let us go and dwell in the villages ) by K. K. Sudhakaran ( 1986 ).
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 K be a topological field, namely a field with a topology such that addition, multiplication, and division are continuous.
Let X be a topological vector space over K. Namely, X is a K vector space equipped with a topology so that vector addition and scalar multiplication are continuous.
Let V be a vector space over a field K, and let be a quadratic form on V. In most cases of interest the field K is either R, C or a finite field.
Let the field K be the set R of real numbers, and let the vector space V be the Euclidean space R < sup > 3 </ sup >.
Let K be the set C of all complex numbers, and let V be the set C < sub > C </ sub >( R ) of all continuous functions from the real line R to the complex plane C.
Let K be R, C, or any field, and let V be the set P of all polynomials with coefficients taken from the field K.
Let the field K be the set R of real numbers, and let the vector space V be the Euclidean space R < sup > 3 </ sup >.
Let K be a closed subset of a compact set T in R < sup > n </ sup > and let C < sub > K </ sub > be an open cover of K. Then
Let and be
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 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 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 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 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 it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.
Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.
Let and rational
Let be a complex rational function from the plane into itself, that is,, where and are complex polynomials.
Let k be a field ( such as the rational numbers ) and K be an algebraically closed field extension ( such as the complex numbers ), consider the polynomial ring kX < sub > n </ sub > and let I be an ideal in this ring.
Let be a real number transcendental over the field of rational numbers, and let be a real number transcendental over, and so on to which is transcendental over.
It can be proved as follows: Let S be a non-empty subset of R and U be an upper bound for S. Substituting a larger value if necessary, we may assume U is rational.
Let Q denote the set of rational numbers, and let d be a square-free integer ( i. e., a product of distinct primes ) other than 1.
Let q < sub > 1 </ sub >, q < sub > 2 </ sub >, ... be an enumeration of the rational numbers in 1 ( recall that the rational numbers are countable ).
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