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 A be the arithmetic mean and H be the harmonic mean of n positive real numbers.

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 be the probability that a certain coin lands heads up ( H ) when tossed.

Let G and H be groups, and let φ: G → H be a homomorphism.

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 H be the hashing function and m the message:

Let gas 1 be H < sub > 2 </ sub > and gas 2 be O < sub > 2 </ sub >.

Let A and H be groups and Ω a set with H acting on it.

Let us assume that H < sub > f </ sub > is in this time complexity class, and we will attempt to reach a contradiction.

Let p ( n ; H ) be the probability that during this experiment at least one value is chosen more than once.

Let n ( p ; H ) be the smallest number of values we have to choose, such that the probability for finding a collision is at least p. By inverting this expression above, we find the following approximation

Let Q ( H ) be the expected number of values we have to choose before finding the first collision.

Let U be a unitary operator on a Hilbert space H ; more generally, an isometric linear operator ( that is, a not necessarily surjective linear operator satisfying ‖ Ux ‖

Let the coin tosses be represented by a sequence of independent random variables, each of which is equal to H with probability p, and T with probability Let N be time of appearance of the first H ; in other words,, and If the coin never shows H, we write N is itself a random variable because it depends on the random outcomes of the coin tosses.

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??

The Supremes, The group that made Ross famous and without which there probably wouldn't be any Diana Ross, scored a handful of hits in the disco clubs without Ross, most notably 1976's " I'm Gonna Let My Heart Do the Walking " and, their last charted single before disbanding, 1977's " You're My Driving Wheel ".

Let function composition interpret group multiplication, and function inverse interpret group inverse.

Let function composition, notated by infix, interpret the group operation.

" Let there arise from you a group of people inviting to what is good, enjoining what is right, and forbidding what is wrong ; these are the ones who will be successful.

It is unclear which version of the paradox is stronger .< ref group =" Note "> Let be the number of civilizations ( per unit volume ) that can be seen at a radius.

A discussion group called Let Lawrence Live was formed by the English department at the university and dozens from the Humanities department gathered on the Kansas campus in front of the Memorial Campanile and lit candles in a peace vigil.

Let S be the group of all permutations of N, the natural numbers, that fixes all but finitely many numbers then:

Let G be a group.

Let G be a group.

Sylows ' test: Let n be a positive integer that is not prime, and let p be a prime divisor of n. If 1 is the only divisor of n that is equal to 1 modulo p, then there does not exist a simple group of order n.

In 1988, the group released the album Let It Be, featuring cover versions of all the songs from the Beatles album of the same name, with the exception of the title track, which they did not record owing to lack of studio time, and " Maggie Mae ", which was replaced by the German anthems " Auf der Lüneburger Heide " and " Was Gleicht Wohl Auf Erden ".

On the Let it Be album where Preston's performances are used the song credits list " with Billy Preston ", clearly identifying him as separate from the main group, yet also giving him a level of individuality that separated him from studio session players.

Let A be an abelian group and f and g be two group homomorphisms from A into itself.

Suppose G is an ordered abelian group, meaning an abelian group with a total ordering "<" respecting the group's addition, so that a < b if and only if a + c < b + c for all c. Let I be a well-ordered subset of G, meaning I contains no infinite descending chain.

According to the jacket notes of the Let Freedom Sing CD set, Crothers was part of the music group The Ramparts who sang A. C. Bilbrew's " The Death of Emmett Till ".

Originally known as The Hi-Fi's, the group changed its name to The 5th Dimension in late 1966 and was best-known during the late 1960s and early 1970s for popularizing the hits " Up, Up and Away ", " Stoned Soul Picnic ", " Aquarius / Let the Sunshine In ", " Wedding Bell Blues ", " One Less Bell to Answer ", "( Last Night ) I Didn't Get to Sleep at All ", and The Magic Garden LP.

The group performed and sang a medley consisting of " What the World Needs Now Is Love " and The Beatles ' " All You Need Is Love " on 23 February 1969 and performed and sang " Aquarius / Let the Sunshine In " on 18 May 1969, the day after the medley fell from the Hot 100 summit.

The group came back for the last fifteen minutes of the show and sang their hits " Up, Up and Away ", " One Less Bell to Answer ", " Stoned Soul Picnic ", " Wedding Bell Blues ", and finished up with " Aquarius / Let the Sunshine In ".

Even though group member Geri Halliwell had returned to the group at this point, she does not take part in this song as with " Let Love Lead the Way ", which signals her departure from the group in the concert's storyline ( performing " Viva Forever " when Geri is leveled under the stage ).