[permalink] [id link]

Formally, given two partially ordered sets ( S, ≤) and ( T, ≤), a function f: S → T is an order-embedding if f is both order-preserving and order-reflecting, i. e. for all x and y in S, one has

from
Wikipedia

## Some Related Sentences

Formally and given

__Formally__

__given__to bishop Philip of Senj

**,**the permission to use the Glagolitic liturgy

**(**the Roman Rite conducted

**in**Slavic language instead of Latin

**,**not the Byzantine rite ), actually extended to

**all**Croatian lands

**,**mostly along the Adriatic coast

**.**

__Formally__

**,**we are

__given__

**a**set of hypotheses

**and**

**a**set of manifestations ; they are related by the domain knowledge

**,**represented by

**a**

**function**that takes as

**an**argument

**a**set of hypotheses

**and**gives as

**a**result the corresponding set of manifestations

**.**

__Formally__

**,**the statement that " value decreases over time "

**is**

__given__by defining the linear differential operator as

**:**

__Formally__

**,**it

**is**

**a**norm defined on the space of bounded linear operators between

**two**

__given__normed vector spaces

**.**

__Formally__

**,**the problem can be stated as follows

**:**

__given__

**a**desired property

**,**expressed as

**a**temporal logic formula p

**,**

**and**

**a**structure M with initial state s

**,**decide

**if**

**.**

__Formally__

**,**

__given__

**two**categories C

**and**D

**,**

**an**equivalence of categories consists of

**a**functor F

**:**C

**→**D

**,**

**a**functor G

**:**D

**→**C

**,**

**and**

**two**natural isomorphisms ε

**:**FG

**→**I < sub > D </ sub >

**and**η

**:**I < sub > C </ sub >→ GF

**.**

__Formally__

**,**

**an**absolute coequalizer of

**a**pair

**in**

**a**category C

**is**

**a**coequalizer as defined above but with the added property that

__given__any functor F

**(**Q ) together with F

**(**q )

**is**the coequalizer of F

**(**

**f**)

**and**F

**(**g )

**in**the category D

**.**Split coequalizers are examples of absolute coequalizers

**.**

__Formally__

**,**

__given__

**a**

**partially**

**ordered**set

**(**P

**,**

**≤),**then

**an**element g of

**a**subset

**S**of P

**is**the greatest element of

**S**

**if**

__Formally__

**,**

**a**deterministic algorithm computes

**a**mathematical

**function**;

**a**

**function**

**has**

**a**unique value

**for**any

__given__input

**,**

**and**the algorithm

**is**

**a**process that produces this particular value as output

**.**

__Formally__

**,**

__given__

**a**finite set X

**,**

**a**collection C of subsets of X

**,**

**all**of size n

**,**

**has**Property B

**if**we can partition X into

**two**disjoint subsets Y

**and**Z such that every set

**in**C meets

**both**Y

**and**Z

**.**

__Formally__

**,**

__given__

**a**graph G

**,**

**a**vertex labeling

**is**

**a**

**function**mapping vertices of G to

**a**set of labels

**.**

__Formally__this mission was declared to be only

**in**pursuit of the Russian vessels

**and**ammunition taken to Anzali by the White Russian counter-revolutionary General Denikin

**,**who had been

__given__asylum by British forces

**in**Anzali

**.**

__Formally__

**,**

**a**married or widowed woman can be called by the

__given__name of her husband

**(**Madame

**(**

__given__name of husband ) family name or Madame veuve

**(**

__given__name of husband ) family name ); this

**is**now slightly out of fashion

**.**

Formally and two

__Formally__

**,**the Congress serves

__two__functions

**:**to approve changes to the Party constitution regarding policy

**and**to elect

**a**Central Committee

**,**about 300 strong

**.**

__Formally__

**,**these failed when they were rejected by the Church of England's General Synod

**in**1972 ; conversations

**and**co-operation continued

**,**however

**,**leading

**in**2003 to the signing of

**a**covenant between the

__two__churches

**.**

__Formally__

**,**we start with

**a**category C with finite products

**(**

**i**

**.**

**e**

**.**C

**has**

**a**terminal object 1

**and**any

__two__objects of C have

**a**product ).

__Formally__

**,**this means symmetry under

**a**sub-group of the Euclidean group of isometries

**in**

__two__or three dimensional Euclidean space

**.**

__Formally__

**,**EMF

**is**classified as the external work expended per unit of charge to produce

**an**electric potential difference across

__two__open-circuited terminals

**.**

__Formally__

**,**

**an**elliptic

**function**

**is**

**a**

**function**meromorphic on

**for**which there exist

__two__non-zero complex numbers

**and**with

**(**

**in**other words

**,**not parallel ), such that

**and**

**for**

**all**

**.**

__Formally__

**,**

__two__variables are inversely proportional

**(**or varying inversely

**,**or

**in**inverse variation

**,**or

**in**inverse proportion or

**in**reciprocal proportion )

**if**

**one**of the variables

**is**directly proportional with the multiplicative inverse

**(**reciprocal ) of the other

**,**or equivalently

**if**their product

**is**

**a**constant

**.**

**(**

__Formally__speaking

**,**this then satisfies the premises of

**an**axiom of well-founded induction

**,**which asserts that these

__two__conditions are sufficient

**for**the proposition to hold

**for**

**all**

**x**

**.**

__Formally__

**,**

**a**Lie superalgebra

**is**

**a**

**(**nonassociative ) Z < sub > 2 </ sub >- graded algebra

**,**or superalgebra

**,**over

**a**commutative ring

**(**typically R or C ) whose product

**,**called the Lie superbracket or supercommutator

**,**satisfies the

__two__conditions

**(**analogs of the usual Lie algebra axioms

**,**with grading ):

__Formally__

**,**the poem can be understood as the combination of

__two__sonnets

**,**though the spacing of the stanzas

**is**irregular

**.**

__Formally__

**,**

**a**vertex cover of

**a**graph G

**is**

**a**set C of vertices such that each edge of G

**is**incident to at least

**one**vertex

**in**C

**.**The set C

**is**said to cover the edges of G

**.**The following figure shows examples of vertex covers

**in**

__two__graphs

**(**

**and**the set C

**is**marked with red ).

__Formally__

**,**he says

**,**the piece consists of

__two__parts of nearly equal length

**,**the end of the first section being bars 24 – 28

**(**p

**.**77 ).

__Formally__known as " Brooks Institute of Photography ," Brooks Institute offers four majors

**,**

__two__certificate programs

**and**

__two__graduate programs

**.**

0.121 seconds.