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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.

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## Some Related Sentences

Formally and sequence

__Formally__

**,**

**a**system

**is**said to be observable

**if**

**,**

**for**any possible

__sequence__

**of**state and control vectors

**,**

**the**current state can be determined in finite time using only

**the**outputs ( this definition

**is**slanted towards

**the**state space representation ).

__Formally__

**,**

**a**byte stream

**is**

**a**certain abstraction

**,**

**a**communication channel down

**which**one entity can send

**a**

__sequence__

**of**bytes to

**the**entity on

**the**other end

**.**

__Formally__

**,**

**the**normal bundle to N in M

**is**

**a**quotient bundle

**of**

**the**tangent bundle on M

**:**one has

**the**short exact

__sequence__

**of**vector bundles on N

**:**

Formally and partial

__Formally__

**,**they are

__partial__derivatives

**of**

**the**option price with respect to

**the**independent variables ( technically

**,**one Greek

**,**gamma

**,**

**is**

**a**

__partial__derivative

**of**another Greek

**,**called delta ).

Formally and some

__Formally__

**,**bending modulus

**is**defined as

**the**energy required to deform

**a**membrane from its intrinsic curvature to

__some__other curvature

**.**

__Formally__

**,**this means that

**,**

**for**

__some__function f

**,**

**the**image f ( D )

**of**

**a**directed set D ( i

**.**e

**.**

**the**set

**of**

**the**images

**of**each element

**of**D )

**is**again directed and has as

**a**least upper bound

**the**image

**of**

**the**least upper bound

**of**D

**.**One could also say that f preserves directed suprema

**.**

__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

**.**

By 1912

**,****the**Social Democrats**,**with an explicitly anti-antisemitic program**,**were**the**largest party in**the**German Reichstag**,**and**the**Progressives ran very strongly as well ...__Formally__**,**at least**,****the**Jews had been fully emancipated with**the**establishment**of****the**German Empire**,**although they were kept out**of**certain influential occupations**,**enjoyed extraordinary prosperity ... Germans intermarried with Jews**:**in**the**1930s__some__50**,**000 Jews were living in mixed German-Jewish marriages**,**so at least 50**,**000 Germans**,**and presumably parts**of**their families**,**had familial contact with**the**Jews**.**__Formally__

**,**we begin by considering

__some__family

**of**distributions

**for**

**a**random variable

**X**

**,**that

**is**indexed by

__some__θ

**.**

__Formally__

**,**Liouville numbers and elementary numbers contain

**the**algebraic numbers

**,**and they include

__some__but not

**all**transcendental numbers

**.**

__Formally__

**,**rotational symmetry

**is**symmetry with respect to

__some__or

**all**rotations in m-dimensional Euclidean space

**.**

__Formally__

**,**

**the**definition only requires

__some__invertibility

**,**so we can substitute

**for**Q any matrix M whose eigenvalues do not include − 1

**.**

__Formally__

**,**

**all**members

**of**

**the**Ghelani family are Hindu Leuva Patel

**,**although

__some__

**have**since chosen other religious beliefs

**.**

Bābak Khorram-Din (

__Formally__known as " Pāpak " meaning " Young Father ") (, alternative spelling**:**Bābak Xorramdin ; 795**,**according to__some__other sources 798 — January 838 ) was one**of****the**main PersianArmenian historian Vardan Areweltsʻi**,**ca**.**__Formally__

**,**

**a**strongly continuous semigroup

**is**

**a**representation

**of**

**the**semigroup ( R < sub >+</ sub >,+) on

__some__Banach space

**X**that

**is**continuous in

**the**strong operator topology

**.**

Formally and infinite

__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__

**,**

**the**question

**of**whether

**the**universe

**is**

__infinite__or finite

**is**whether it

**is**an unbounded or bounded metric space

**.**

__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__

**,**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__

**,**assuming our intuition from

**the**finite dimensional case carries over into

**the**

__infinite__dimensional setting

**,**

**the**measure should then be equal to

Formally and if

__Formally__

**,**oxidation state

**is**

**the**hypothetical charge that an atom would

**have**

__if__

**all**bonds to atoms

**of**different elements were 100 % ionic

**.**

__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__

**,**

__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__

**,**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**decision problem

**is**P-complete ( complete

**for**

**the**complexity class P )

__if__it

**is**in P and that

**every**problem in P can be reduced to it by using an appropriate reduction

**.**

If R

**is****a**ring**,**let R denote**the**ring**of**polynomials in**the**indeterminate**X**over R**.**Hilbert proved that__if__R**is**" not too large ", in**the**sense that__if__R**is**Noetherian**,****the****same**must be true**for**R**.**__Formally__**,**__Formally__

**,**

**a**hypothesis

**is**compared against its opposite or null hypothesis ("

__if__I release this ball

**,**it will not fall to

**the**floor ").

__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__

**,**

__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__

**,**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

**.**

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**.**__Formally__

**,**

__if__we write F < sub > Δ </ sub >( x ) to mean

**the**f-polynomial

**of**Δ

**,**then

**the**h-polynomial

**of**Δ

**is**

__Formally__

**,**

**a**cardinal κ

**is**defined to be weakly compact

__if__it

**is**uncountable and

**for**

**every**function f

**:**< sup > 2 </ sup > →

0.188 seconds.