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Page "Limit (category theory)" ¶ 87
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Let and I
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 us focus on an atom of calcium from the tip of the bone of my finger and let us suppose that I swallow a magic Alice In Wonderland growing pill.
For a compilation album of the Glenmark duo Gemini, Andersson had Björn Ulvaeus write new Swedish lyrics for the re-recording of two old songs ; Ulvaeus also wrote new English lyrics to older Swedish language songs for opera singer Anne Sofie von Otter tribute album " I Let The Music Speak ".
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 >.
* Phone number, slang as digit, as in " Let me get your digits so I can call you tonight.
" Let me in, I love you!
The sentiment is summarized in a line from Ovid's Amores I. 1. 27 Sex mihi surgat opus numeris, in quinque residat-" Let my work rise in six steps, fall back in five.
Records such as " Let Me Be the One " by Safire, " I Remember What You Like " by Jenny Burton, " Running " by Information Society, " Give Me Tonight " by Shannon and " It Works For Me " by Pam Russo enjoyed heavy New York radio airplay.
Gloria Gaynor ( born September 7, 1949 ) is an American singer, best known for the disco era hits ; " I Will Survive " ( Hot 100 number 1, 1979 ), " Never Can Say Goodbye " ( Hot 100 number 9, 1974 ), " Let Me Know ( I Have a Right )" ( Hot 100 number 42, 1980 ) and " I Am What I Am " ( R & B number 82, 1983 ).
In late 1979, she released the album I Have a Right which contained her next disco hit, " Let Me Know ( I Have a Right )", which featured Doc Severinsen of The Tonight Show fame, on trumpet solo.
After telling the audience " I shall now read to you the scroll of the Establishment of the State, which has passed its first reading by the National Council ", Ben-Gurion proceeded to read out the declaration, taking 16 minutes, ending with the words " Let us accept the Foundation Scroll of the Jewish State by rising " and calling on Rabbi Fishman to recite the Shehecheyanu blessing.
Let ( I, ≤) be a directed poset ( not all authors require I to be directed ).
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 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 and be
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 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 and finite
* 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 )
Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.
Let X be a finite set with n elements.
Let there be a finite sequence of positive integers X
Let Σ be an alphabet, a non-empty finite set.
Let Σ be an alphabet ( finite set ).
Let be a random sample of size n — that is, a sequence of independent and identically distributed random variables drawn from distributions of expected values given by µ and finite variances given by σ < sup > 2 </ sup >.
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 E be the set of real numbers that can be defined by a finite number of words.
Let K be a number field ( i. e., a finite extension of ), in other words, for some by the primitive element theorem.
Let be a finite 2-dimensional pseudo-manifold.
Theorem: Let R be a Dedekind domain with fraction field K. Let L be a finite degree field extension of K and denote by S the integral closure of R in L. Then S is itself a Dedekind domain.
Let M be the intersection of all subgroups of the free Burnside group B ( m, n ) which have finite index, then M is a normal subgroup of B ( m, n ) ( otherwise, there exists a subgroup g < sup >-1 </ sup > Mg with finite index containing elements not in M ).
Let Σ be a finite set ( an " alphabet ") and let A be the set of all regular expressions over Σ.
Let X be a random variable with finite expected value μ and finite non-zero variance σ < sup > 2 </ sup >.
Let X < sub > 1 </ sub > and X < sub > 2 </ sub > be two random variables with means and finite variances of μ < sub > 1 </ sub > and μ < sub > 2 </ sub > and σ < sub > 1 </ sub > and σ < sub > 2 </ sub > respectively.
Let be the category of finite sets and bijections ( the collection of all finite sets, and invertible functions between them ).
Let S be a family of finite sets, where the family may contain an infinite number of sets and the individual sets may be repeated multiple times.
Let X be a locally compact Hausdorff space equipped with a finite Radon measure μ, and let Y be a σ-compact Hausdorff space with a σ-finite Radon measure ρ.
Let X be the set N of natural numbers, and let a subset of N be negligible if it is finite.

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