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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 ).

from
Wikipedia

## Some Related Sentences

Formally and collective

__Formally__

**a**member

**of**the country's

__collective__head

**of**state

**and**

**,**

**as**president

**of**parliament

**,**holder

**of**the third-highest office

**,**he was left with little political influence.

Formally and noun

__Formally__

**,**the verbal

__noun__

**(**VN

**,**still retaining verbal characteristics ) takes okurigana

**,**

**as**is usual

**for**verbs

**,**while the deverbal

__noun__

**(**DVN

**,**without verbal characteristics ) does not take okurigana

**,**

**as**is usual

**for**nouns.

Formally and forms

__Formally__

**,**it refers to

**a**set

**of**six verb

__forms__inflected

**for**person

**and**number forming

**a**single paradigm.

Formally and such

__Formally__the " head

**of**state " can also personally be the " head

**of**government "

**(**ex officio

**or**

**by**ad hoc cumulation

__such__

**as**an absolute monarch nominating himself ) but otherwise has formal precedence over the Head

**of**Government

**and**other ministers

**,**whether he is their actual political superior

**(**absolute monarch

**,**executive president )

**or**rather theoretical

**or**ceremonial

**in**character.

__Formally__

**,**the theorem is stated

**as**follows: There exist unique integers q

**and**r

__such__that

**a**= qd + r

**and**0 ≤ r < | d |, where | d | denotes the absolute value

**of**d.

__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__

**,**cl

**(**S ) denotes the smallest subset Y

**of**M that contains S

__such__that

**for**each reaction

**(**A

**,**B )

__Formally__

**,**the word is applied to persons who

**are**publicly accepted

**in**

**a**recognised capacity

**,**

__such__

**as**professional employment

**,**graduation from

**a**course

**of**study

**,**etc., to give critical commentaries

**in**one

**or**any

**of**

**a**number

**of**specific fields

**of**public

**or**private achievement

**or**endeavour.

__Formally__

**,**the case where only

**a**subset

**of**parameters is defined is still

**a**composite hypothesis ; nonetheless

**,**the term point hypothesis is often applied

**in**

__such__cases

**,**particularly where the hypothesis test can be structured

**in**

__such__

**a**way that the distribution

**of**the test statistic

**(**the distribution under the null hypothesis ) does not depend on the parameters whose values have not been specified under the point null hypothesis.

__Formally__

**,**

**a**measurable cardinal is an uncountable cardinal number κ

__such__that there exists

**a**κ-additive

**,**non-trivial

**,**0-1-valued measure on the power set

**of**κ.

__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__

**,**

**a**coalgebra over

**a**field K is

**a**vector space C over K together with K-linear maps Δ: C → C ⊗ C

**and**ε: C → K

__such__that

__Formally__

**,**

**a**Hopf algebra is

**a**

**(**associative

**and**coassociative ) bialgebra H over

**a**field K together with

**a**K-linear map S: H → H

**(**called the antipode )

__such__that the following diagram commutes:

__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__

**a**congruence subgroup is one that contains Γ

**(**N )

**for**some N

**,**

**and**the least

__such__N is the level

**or**Stufe

**of**the subgroup.

__Formally__

**,**knowing the step response

**of**

**a**dynamical system gives information on the stability

**of**

__such__

**a**system

**,**

**and**on its ability to reach one stationary state when starting from another.

__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__

**,**

**a**cardinal number κ is λ-unfoldable if

**and**only if

**for**every transitive model M

**of**cardinality κ

**of**ZFC-minus-power set

__such__that κ is

**in**M

**and**M contains all its sequences

**of**length less than κ

**,**there is

**a**non-trivial elementary embedding j

**of**M into

**a**transitive model with the critical point

**of**j being κ

**and**j

**(**κ ) ≥ λ.

__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__

**,**we define

**a**bad field

**as**

**a**structure

**of**the form

**(**K

**,**T ), where K is an algebraically closed field

**and**T is an infinite

**,**proper

**,**distinguished subgroup

**of**K

**,**

__such__that

**(**K

**,**T ) is

**of**finite Morley rank

**in**its full language.

Formally and “

__Formally__the neutral is called the

__“__grounded conductor ”;

**as**

**of**the 2008 NEC

**,**the terms

__“__neutral conductor

**”**

**and**

__“__neutral point

**”**have been defined

**in**the Code to record what had been common usage.

__Formally__

**,**Spanish naming customs conflate his name

__“__George

**”**

**and**his middle-name

__“__Albert

**”**to the composite name

__“__George Albert ”,

**and**his sole surname

**,**

__“__Duran ”, is duplicated

**as**his paternal

**and**maternal surnames.

__“__

__Formally__stated

**,**interactivity is an expression

**of**the extent that

**in**

**a**given series

**of**communication exchanges

**,**any third

**(**

**or**later ) transmission

**(**

**or**message ) is related to the degree to

**which**previous exchanges referred to even earlier transmissions

**”**

**(**Sheizaf Rafaeli

**,**

__“__Interactivity

**,**From New Media to Communication ,” pages 110-34

**in**Advanced Communicational Science: Merging Mass

**and**Interpersonal Processes

**,**ed.

Formally and group

__Formally__

**,**

**a**profinite

__group__is

**a**Hausdorff

**,**compact

**,**

**and**totally disconnected topological

__group__: that is

**,**

**a**topological

__group__that is also

**a**Stone space.

__Formally__

**,**this means symmetry under

**a**sub-group

**of**the Euclidean

__group__

**of**isometries

**in**two

**or**three dimensional Euclidean space.

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.
* Blades

**(**hip-hop__group__)**(**__Formally__Blades Of Hades ), Australian hip hop__group__from Newcastle**,**New South Wales__Formally__

**,**

**a**frieze

__group__is

**a**class

**of**infinite discrete symmetry groups

**for**patterns on

**a**strip

**(**infinitely wide rectangle ), hence

**a**class

**of**groups

**of**isometries

**of**the plane

**,**

**or**

**of**

**a**strip.

__Formally__

**,**the

__group__was called Studiengesellschaft für Geistesurgeschichte ‚ Deutsches Ahnenerbe e. V.

__Formally__

**,**the Mahalanobis distance

**of**

**a**multivariate vector from

**a**

__group__

**of**values with mean

**and**covariance matrix is defined

**as**:

__Formally__

**,**let G be

**a**Coxeter

__group__with reduced root system R

**and**k < sub > v </ sub >

**a**multiplicity function on R

**(**so k < sub > u </ sub > = k < sub > v </ sub > whenever the reflections σ < sub > u </ sub >

**and**σ < sub > v </ sub > corresponding to the roots u

**and**v

**are**conjugate

**in**G

**).**

__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__Roman Kalyn is now the only member

**of**the

__group__

**,**but de-facto GreenJolly exists

**in**name only.

__Formally__

**,**

**a**redistribution

**of**all agents ’ initial endowments

**of**goods among all agents

**in**the system is

**a**core allocation if no

__group__

**of**agents can redistribute their own initial endowments among themselves so

**as**to improve the satisfaction

**of**someone

**in**the

__group__without impairing that

**of**any other

**in**the

__group__.

__Formally__

**,**this meant that the whole peloton finished out

**of**time limits

**,**but the referees understandably used

**a**rule saying that they could give clemency to any

__group__

**of**more than 20 %

**of**the stage's starting riders

**,**officially citing the weather conditions

**as**their reason to do so.

__Formally__

**,**

**a**signed graph Σ is

**a**pair

**(**G

**,**σ ) that consists

**of**

**a**graph G =

**(**V

**,**E )

**and**

**a**sign mapping

**or**signature σ from E to the sign

__group__

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