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( 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.

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## Some Related Sentences

Formally and speaking

__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__

__speaking__

**,**

**the**strategy pattern defines a family

**of**algorithms

**,**encapsulates each one

**,**and makes them interchangeable

**.**

__Formally__

__speaking__

**,**

**the**opportunity was extended

**to**

**all**classes

**to**join China's project on its Leninist terms

**.**

Formally and then

__Formally__

**,**if d is

**the**dimension

**of**

**the**parameter

**,**and n is

**the**number

**of**samples

**,**if as and as

**,**

__then__

**the**model is semi-parametric

**.**

__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__declared on October 9

**,**1970

**,**

**the**Khmer Republic was a right-wing pro-United States military-led government headed by General Lon Nol and Prince Sisowath Sirik Matak

**that**took power in

**the**March 18

**,**1970 coup against Prince Norodom Sihanouk

**,**

__then__

**the**country's head

**of**state

**.**

__Formally__

**,**if we write F < sub > Δ </ sub >(

**x**)

**to**mean

**the**f-polynomial

**of**Δ

**,**

__then__

**the**h-polynomial

**of**Δ is

* General Headquarters United Nations Command

**(**Korea )**(**UNC ) —__Formally__activated 10 July 1950**,**before__then__Allied forces were formally under American operational control**.**__Formally__it consists

**of**three groups

**of**four measure phrases

**of**three

**to**four chords repeated four times each

**,**ABC :|| ABC

**,**

**which**

__then__merges with

**the**next movement

**,**" Floe " with

**the**entrance

**of**

**the**horns

**.**

__Formally__

**,**if T is a complete

**sufficient**statistic

**for**θ and E

**(**g

**(**T )) = τ

**(**θ )

__then__g

**(**T ) is

**the**minimum-variance unbiased estimator

**(**MVUE )

**of**τ

**(**θ ).

__Formally__

**,**if R is a Noetherian ring and I is a principal

**,**proper ideal

**of**R

**,**

__then__I has height at most one

**.**

__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__

**,**define

**the**set

**of**lines in

**the**plane P as L

**(**P );

__then__a rigid motion

**of**

**the**plane takes lines

**to**lines –

**the**group

**of**rigid motions acts on

**the**set

**of**lines – and one may ask

**which**lines

**are**unchanged by

**an**action

**.**

__Formally__

**,**if f is a harmonic function

**,**

__then__f cannot exhibit a true local maximum within

**the**domain

**of**definition

**of**f

**.**In other words

**,**either f is a constant function

**,**or

**,**

**for**any point inside

**the**domain

**of**f

**,**there exist other points arbitrarily close

**to**at

**which**f takes larger values

**.**

__Formally__

**,**if we denote

**the**set

**of**stable functions by S

**(**D ) and

**the**stability radius by r

**(**f

**,**D ),

__then__:

__Formally__

**,**assuming our intuition from

**the**finite dimensional case carries over into

**the**infinite dimensional setting

**,**

**the**measure should

__then__be equal

**to**

Formally and satisfies

__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__

__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**game

**(**coalitional game ) consists

**of**a finite set

**of**players

**,**called

**the**grand coalition

**,**and a characteristic function denotes

**the**power set

**of**.</ ref > from

**the**set

**of**

**all**possible coalitions

**of**players

**to**a set

**of**payments

**that**

__satisfies__

**.**

__Formally__

**,**a biased graph Ω is a pair

**(**G

**,**B ) where B is a linear class

**of**circles ;

**this**by definition is a class

**of**circles

**that**

__satisfies__

**the**theta-graph property mentioned above

**.**

Formally and axiom

__Formally__

**,**assuming

**the**

__axiom__

**of**choice

**,**cardinality

**of**a set X is

**the**least ordinal α such

**that**there is a bijection between X and α

**.**

Formally and which

__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

**.**

However

**,**shortly after**this**positive result**,**Kurt Gödel published On__Formally__Undecidable Propositions**of**Principia Mathematica and Related Systems**(**1931 ), showing**that**in any sufficiently strong axiomatic system there**are**true statements__which__cannot be proved in**the**system**.**__Formally__

**,**a frame is defined

**to**be a lattice L in

__which__finite meets distribute over arbitrary joins

**,**i

**.**e

**.**every

**(**even infinite ) subset

__Formally__

**,**collective noun forms such as “ a group

**of**people ”

**are**represented by second-order variables

**,**or by first-order variables standing

**for**sets

**(**

__which__

**are**well-defined objects in mathematics and logic ).

__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__

**,**

**the**sequence

**of**partial sums

**of**some infinite summation converges if

**for**every fixed power

**of**X

**the**coefficient stabilizes: there is a point beyond

__which__

**all**further partial sums have

**the**same coefficient

**.**

__Formally__

**,**a unique factorization domain is defined

**to**be

**an**integral domain R in

__which__every non-zero and non-unit

**x**

**of**R can be written as a product

**(**including

**an**empty product )

**of**irreducible elements p < sub > i </ sub >

**of**R and a unit u:

__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**

**.**

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__

**,**dependence refers

**to**any situation in

__which__random variables do not satisfy a mathematical condition

**of**probabilistic independence

**.**

__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__

**,**

**this**follows from

**the**convolution theorem in mathematics

**,**

__which__relates

**the**Fourier transform

**of**

**the**power spectrum

**(**

**the**intensity

**of**each frequency )

**to**its autocorrelation

**.**

__Formally__known as Motion Picture Distribution LP

**,**it was re branded and relaunched in 2007 due

**to**

**the**break-up

**of**its preceding company

**,**Alliance Atlantis

**,**

__which__was sold off piece by piece

**to**Canwest Global

**,**GS Capital Partners

**,**along with several other smaller companies

**.**

__Formally__

**,**a rigged Hilbert space consists

**of**a Hilbert space H

**,**together with a subspace Φ

__which__carries a finer topology

**,**

**that**is one

**for**

__which__

**the**natural inclusion

__Formally__known as

**the**Inverurie Parish Church

**,**a split in Church

**of**Scotland over

**the**appointment

**of**ministers in 1843

**(**The Disruption ) led

**to**

**the**creation

**of**

**the**West Parish Church

**(**known locally as " The West Kirk ")

__which__was founded as a Free Church

**(**a church free from Edinburgh control ) thus causing

**the**Inverurie Parish Church

**to**change its name

**.**

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