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

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 < sup >∞</ sup >( M ) vanishing at x, and let I < sub > x </ sub >< sup > 2 </ sup > be the set of functions of the form, where f < sub > i </ sub >, g < sub > i </ sub > ∈ I < sub > x </ sub >.

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.

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 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 < sup > op </ sup > → C be a diagram.

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

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 the savages kill each other.

Let it burn down.

Let Senora Brannon live in her father's house for a time.

Let me pass over the trip to Sante Fe with something of the same speed which made Mrs. Roebuck `` wonduh if the wahtahm speed limit '' ( 35 m.p.h. ) `` is still in ee-faket ''.

Let me set the record this time, and let me get back OK, so the German will give me the exclusive.

Let us look in on one of these nerve centers -- SAC at Omaha -- and see what must still happen before a wing of B-52 bombers could drop their Aj.

Let me quote him even more fully, for his analysis is important to my theme.

Let us re-examine the publicized contrasts between Ptolemaic and Copernican astronomy.

Let us not confuse the issue by labeling the objective or the method `` psychoanalytic '', for this is a well established term of art for the specific ideas and procedures initiated by Sigmund Freud and his followers for the study and treatment of disordered personalities.

Let us differentiate a few of these ideas.

Let us survey for a moment the development of modern thought -- turning our attention from the Reformation toward the revolutionary and romantic movements that follow and dwelling finally on more recent decades.

`` Let him become honest, and they discard him.

Let me give Papa blood ''.

Let us now give some thought to the soul.

Let me then ( and in public ) glance into the mirror.

Let us see just how typical Krim is.

Let him bounce back, and he could really set up the staff.

Let us prepare for peace, instead of for a war which would mean the end of civilization.

Let us have more benches and fewer forbidden areas around fountains and gardens.

Let us, like the French, have outdoor cafes where we may relax, converse at leisure and enjoy the passing crowd.

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.

One means to help the birds occurs to me: Let the chimes that ring over Washington Square twice daily, discontinue any piece of music but one.

Let them offer on behalf of those creatures whose melody has been the joy of mankind since time began, the hymn `` Abide With Me ''.

Let me tell you what happened to me today.

`` Let me do the submitting to the Royal Academy '', he suggested.

Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.

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.