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Every ordered field is a formally real field.

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## Some Related Sentences

Every and ordered

** Zorn's lemma:

__Every__non-empty partially__ordered__set in which every chain ( i**.**e**.**totally__ordered__subset ) has an upper bound contains at least one maximal element**.**
The restricted principle "

__Every__partially__ordered__set has**a**maximal totally__ordered__subset "**is**also equivalent to AC over ZF**.**__Every__

__ordered__

**field**

**is**

**a**

**formally**

**real**

**field**, i

**.**e., 0 cannot be written as

**a**sum of nonzero squares

**.**

*

__Every__non-empty set of left ideals of R, partially__ordered__by inclusion, has**a**maximal element with respect to set inclusion**.**
*

__Every__totally__ordered__set that**is****a**bounded lattice**is**also**a**Heyting algebra, where**is**equal to when, and 1 otherwise**.**__Every__time she entered, song typical of the Brazilian northeast would play, stopping only when

__ordered__by Cirene herself

**.**

Every and field

__Every__

__field__has an algebraic extension which

**is**algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice

**.**

__Every__time an MTA receives an email message, it adds

**a**< tt > Received </ tt > trace header

__field__to the top of the header of the message, thereby building

**a**sequential record of MTAs handling the message

**.**

__Every__instruction consists of

**a**9-bit opcode,

**a**4-bit register code, and

**a**23-bit effective address

__field__, which consists in turn of

**a**1-bit indirect bit,

**a**4-bit register code, and an 18-bit offset

**.**

__Every__

__field__theory of particle physics

**is**based on certain symmetries of nature whose existence

**is**deduced from observations

**.**

__Every__planetary body ( including the Earth )

**is**surrounded by its own gravitational

__field__, which exerts an attractive force on all objects

**.**

__Every__prime ideal P in

**a**Boolean ring R

**is**maximal: the quotient ring R / P

**is**an integral domain and also

**a**Boolean ring, so it

**is**isomorphic to the

__field__F < sub > 2 </ sub >, which shows the maximality of P

**.**Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings

**.**

__Every__year, the British Political Studies Association awards the Walter Bagehot Prize for the best dissertation in the

__field__of government and public administration

**.**

__Every__polynomial in can be factorized into polynomials that are irreducible over F

**.**This factorization

**is**unique up to permutation of the factors and the multiplication of the factors by nonzero constants from F ( because the ring of polynomials over

**a**

__field__

**is**

**a**unique factorization domain whose units are the nonzero constant polynomials ).

__Every__quadratic form q in n variables over

**a**

__field__of characteristic not equal to 2

**is**equivalent to

**a**diagonal form

__Every__kind of material has unique magnetic properties, even those that we do not think of as being “ magnetic .” Different materials below the ground can cause local disturbances in the Earth ’ s magnetic

__field__that are detectable with sensitive magnetometers

**.**

Every and is

__Every__legislator from Brasstown Bald to Folkston

__is__going to have his every vote subjected to the closest scrutiny as

**a**test of his political allegiances, not his convictions

**.**

__Every__detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he

__is__playing with Viennese musicians ), and the gossamer shading throughout

**.**

__Every__taxpayer

__is__well aware of the vast size of our annual defense budget and most of our readers also realize that

**a**large portion of these expenditures go for military electronics

**.**

__Every__few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it

__is__by ancient brick vaulting

**.**

__Every__dream, and this

__is__true of

**a**mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought,

__is__

**a**psychic phenomenon for which no explanation

__is__available

**.**

__Every__library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it

__is__to hear the librarian say apologetically, `` I'm sorry, but we don't have that book

**.**

__Every__community, if it

__is__alive has

**a**spirit, and that spirit

__is__the center of its unity and identity

**.**

__Every__natural-born citizen of

**a**foreign state who

__is__also an American citizen and every natural-born American citizen who

__is__

**a**citizen of

**a**foreign land owes

**a**double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming

**a**citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming

**a**citizen of another nation ).

__Every__line of written text

__is__

**a**mere reflection of references from any of

**a**multitude of traditions, or, as Barthes puts it, " the text

__is__

**a**tissue of quotations drawn from the innumerable centres of culture "; it

__is__never original

**.**

__Every__year, on the last Sunday in April, there

__is__an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth

**.**

__Every__lattice element of the structure

__is__in its proper place, whether it

__is__

**a**single atom or

**a**molecular grouping

**.**

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