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Formally, a binary operation on a set S is called associative if it satisfies the associative law:

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## Some Related Sentences

Formally and binary

__Formally__

**,**

**a**ring

**is**an Abelian group ( R

**,**+), together with

**a**second

__binary__

**operation*** such that for all

**a**

**,**b and c in R

**,**

__Formally__

**,**an unlabelled state transition system

**is**

**a**tuple (

**S**

**,**→) where

**S**

**is**

**a**

**set**( of states ) and → ⊆

**S**×

**S**

**is**

**a**

__binary__relation over

**S**( of transitions ).

Formally and operation

__Formally__

**,**

**a**mortgage lender ( mortgagee ), or other lien holder

**,**obtains

**a**termination of

**a**mortgage borrower ( mortgagor )' s equitable right of redemption

**,**either by court order or by

__operation__of

**law**( after following

**a**specific statutory procedure ).

__Formally__

**,**

**a**cumulativity predicate CUM can be defined as follows

**,**where capital X

**is**

**a**variable over sets

**,**U

**is**

**the**universe of discourse

**,**p

**is**

**a**mereological part structure

**on**U

**,**and

**is**

**the**mereological sum

__operation__.

__Formally__

**,**LPAR designates

**the**logical partitioning function and mode of

__operation__

**,**whereas PR / SM

**is**

**the**commercial designation of

**the**feature.

Formally and on

__Formally__organized vocational programs supported by federal funds allow high school students to gain experience in

**a**field of work which

**is**likely to lead to

**a**full-time job

__on__graduation.

__Formally__speaking

**,**

**a**collation method typically defines

**a**total order

__on__

**a**

**set**of possible identifiers

**,**

**called**sort keys

**,**which consequently produces

**a**total preorder

__on__

**the**

**set**of items of information ( items with

**the**same identifier are not placed in any defined order ).

__Formally__

**,**

**if**M

**is**

**a**

**set**

**,**

**the**identity function f

__on__M

**is**defined to be that function with domain and codomain M which

**satisfies**

*

**,**see On__Formally__Undecidable Propositions of Principia Mathematica and Related Systems for details__on__English translations.__Formally__

**,**in

**the**finite-dimensional case

**,**

**if**

**the**linear map

**is**represented as

**a**multiplication by

**a**matrix A and

**the**translation as

**the**addition of

**a**vector

**,**an affine map acting

__on__

**a**vector can be represented as

__Formally__

**,**

**a**detailed balanced process

**is**

**the**one

__on__which

**the**probability to be in

**the**state x and transit to x ' must be

**the**same as to be in

**the**state x ' and transit to x.

__Formally__

**,**

**a**function ƒ

**is**real analytic

__on__an open

**set**D in

**the**real line

**if**for any x < sub > 0 </ sub > in D one can write

__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__

**,**

**if**

**is**an open subset of

**the**complex plane

**,**

**a**point of

**,**and

**is**

**a**holomorphic function

**,**then

**is**

**called**

**a**removable singularity for

**if**there exists

**a**holomorphic function which coincides with

__on__.

__Formally__

**,**

**the**appointment remains

**a**royal one made

__on__

**the**advice of

**the**Lord Chancellor

**,**but he / she no longer comments

__on__individual applications

**,**and merely supervises

**the**process and reviews

**the**panel's recommendations in general terms ( satisfying himself / herself that

**the**process as operated

**is**fair and efficient ).

Informally

**,**G has**the**above presentation**if****it****is****the**" freest group " generated by**S**subject only to**the**relations R.__Formally__**,****the**group G**is**said to have**the**above presentation**if****it****is**isomorphic to**the**quotient of**a**free group__on__**S**by**the**normal subgroup generated by**the**relations R.
In late 1900s

**the**day that of**the**City was founded**is**Jakin School**is****a**Private School**is**__Formally__Part of Jakin School Board was Grades One through Twelve there**is**no Football field__on__this school. In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary**,**Junior High**,**and High School ( which later Became Early County High**,**Middle**,**and Elementary School ). while Carver school was built for African-American students grades One through Twelve. although late 1960s when Carver school was closed along with Kestler School was based in Damascus were sent to Washington High & Elementary at Blakely. In addition to small farm agriculture**,**Jakin's early economic growth resulted from turpentine.__Formally__

**,**

**a**center of gravity

**is**an application point of

**the**resultant gravitational force

__on__

**the**body.

__Formally__named The King's College of Our Lady and Saint Nicholas in Cambridge

**,**

**the**college lies

__on__

**the**River Cam and faces out onto King's Parade in

**the**centre of

**the**city.

__Formally__

**,**

**a**statistic s

**is**

**a**measurable function of X ; thus

**,**

**a**statistic s

**is**evaluated

__on__

**a**random variable X

**,**taking

**the**value s ( X ), which

**is**itself

**a**random variable.

__Formally__educated African Americans

**,**

__on__

**the**other hand

**,**either disregarded black minstrelsy or openly disdained

**it**.

__Formally__

**,**

**the**motion merely calls

__on__parliament to thank

**the**monarch or viceroy for

**the**speech via an Address in Reply.

Formally and set

__Formally__

**,**

**the**

__set__of all context-free languages

**is**identical to

**the**

__set__of languages accepted by pushdown automata ( PDA ).

__Formally__

**,**according to

**the**Constitution

**,**citizens of Turkmenistan have

**the**right to

__set__up political parties and other public associations

**,**acting within

**the**framework of

**the**Constitution and laws

**,**and public associations and groups of citizens have

**the**right to nominate their candidates in accordance with

**the**election

**law**.

__Formally__

**,**

**the**convex hull may be defined as

**the**intersection of all convex sets containing X or as

**the**

__set__of all convex combinations of points in X.

__Formally__

**,**

**the**discrete cosine transform

**is**

**a**linear

**,**invertible function ( where denotes

**the**

__set__of real numbers ), or equivalently an invertible N × N square matrix.

__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**movement

**is**

**a**rondo that acts as

**the**theme for

**a**

__set__of eight variations

**,**capped off by

**a**dramatic coda.

__Formally__

**,**

**the**discrete sine transform

**is**

**a**linear

**,**invertible function F

**:**R < sup > N </ sup > < tt >-></ tt > R < sup > N </ sup > ( where R denotes

**the**

__set__of real numbers ), or equivalently an N × N square matrix.

__Formally__

**,**

**the**discrete Hartley transform

**is**

**a**linear

**,**invertible function H

**:**R < sup > n </ sup > < tt >-></ tt > R < sup > n </ sup > ( where R denotes

**the**

__set__of real numbers ).

__Formally__

**,**

**a**constraint satisfaction problem

**is**defined as

**a**triple

**,**where

**is**

**a**

__set__of variables

**,**

**is**

**a**domain of values

**,**and

**is**

**a**

__set__of constraints.

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