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 ( S ,*) be a set S with a binary operation * on it ( known as a magma ).

Proof: Let d be the position of the leftmost ( most significant ) nonzero bit in the binary representation of s, and choose k such that the dth bit of x < sub > k </ sub > is also nonzero.

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

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 be any binary relation over.

Let be a set equipped with two binary operations, which we will write.

Let Rp ( A, a ), meaning " the set a represents the class A ," denote a binary relation defined as follows:

Let be the set of binary variables from monitors and be the set of binary variables from sources.

Let E be a Euclidean space or an integer grid, and A a binary image in E.

A binary image is viewed in mathematical morphology as a subset of a Euclidean space R < sup > d </ sup > or the integer grid Z < sup > d </ sup >, for some dimension d. Let E be a Euclidean space or an integer grid, A a binary image in E, and B a structuring element.

Booth's algorithm can be implemented by repeatedly adding ( with ordinary unsigned binary addition ) one of two predetermined values A and S to a product P, then performing a rightward arithmetic shift on P. Let m and r be the multiplicand and multiplier, respectively ; and let x and y represent the number of bits in m and r.

Let parthood be the defining primitive binary relation of the underlying mereology, and let the atomic formula Pxy denote that " x is part of y ".

Let O, the binary relation of mereological overlap, be defined as:

Let be a binary linear code length.

Let C be a category with binary products and let Y and Z be objects of C. The exponential object Z < sup > Y </ sup > can be defined as a universal morphism from the functor –× Y to Z.

" 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 '~' 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 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 be the set of ordered pairs of integers with not zero, and define an equivalence relation on according to which if and only if.

Let now x ' and y ' be tuples of previously unused variables of the same length as x and y respectively, and let Q be a previously unused relation symbol which takes as many arguments as the sum of lengths of x and y ; we consider the formula

" Walter Neff replies, " No relation ", to which Mr. Jackson says, " Let me see, this man's an automobile dealer in Corvallis.

* is minimal: Let be any transitive relation containing, we want to show that.

Let A be a set ( of the elements of an algebra ), and let E be an equivalence relation on the set A.

Let ( X, R ) be a set-like well-founded relation, and F a function, which assigns an object F ( x, g ) to each pair of an element x ∈ X and a function g on the initial segment

* Let the relation "≤" on

Let Q and P be two self-adjoint operators satisfying the canonical commutation relation, = i, and s and t two real parameters.

Let be a relation in, where.

Let V be a vector space over a field K, and let N be a subspace of V. We define an equivalence relation ~ on V by stating that x ~ y if x − y ∈ N. That is, x is related to y if one can be obtained from the other by adding an element of N. From this definition, one can deduce that any element of N is related to the zero vector ; in other words all the vectors in N get mapped into the equivalence class of the zero vector.

Theodor Estermann ( 1902 – 1991 ) proved in his book Complex Numbers and Functions the following relation: Let be a bounded region with continuous boundary.

The minimal separators also form an algebraic structure: For two fixed vertices a and b of a given graph G, an ( a, b )- separator S can be regarded as a predecessor of another ( a, b )- separator T, if every path from a to b meets S before it meets T. More rigorously, the predecessor relation is defined as follows: Let S and T be two ( a, b )- separators in ' G '.

Let p be a point of M. Consider the space consisting of smooth maps defined in some neighborhood of p. We define an equivalence relation on as follows.

Let Y be an algebraic space defined by an equivalence relation S ⊂ V × V. The set Hom ( Y, X ) of morphisms of algebraic spaces is then defined by the condition that it makes the descent sequence