* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

Every quadratic form q in n variables over a field of characteristic not equal to 2 is equivalent to a diagonal form

Every degree of freedom in the energy is quadratic and, thus, should contribute k < sub > B </ sub > T to the total average energy, and k < sub > B </ sub > to the heat capacity.

** Every vector space has a basis.

** Every infinite game in which is a Borel subset of Baire space is determined.

** Every Tychonoff space has a Stone – Čech compactification.

* Theorem Every reflexive normed space is a Banach space.

Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

* Every topological space X is a dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification.

* Every compact metric space is separable.

* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.

* Pseudocompact: Every real-valued continuous function on the space is bounded.

Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.

Every compact metric space is complete, though complete spaces need not be compact.

Every point in three-dimensional Euclidean space is determined by three coordinates.

Every node on the Freenet network contributes storage space to hold files, and bandwidth that it uses to route requests from its peers.

Every space filling curve hits some points multiple times, and does not have a continuous inverse.

* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )

Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.

Every normed vector space V sits as a dense subspace inside a Banach space ; this Banach space is essentially uniquely defined by V and is called the completion of V.

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 single problem touched on thus far is related to good marketing planning.

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 man in every one of these houses is a Night Rider.

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.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

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 root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

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.

Every Economic union, Customs and monetary union and Economic and monetary union has also a Customs Union

Every president after Lyndon Johnson has also appointed staff to this position.

He has also co-authored Unstoppable Global Warming: Every 1, 500 Years ( 2007 ) with Dennis Avery, and Climate Change Reconsidered ( 2009 ) with Craig Idso.

Every Mac made between 1986 and 1998 has a SCSI port on the back, making external expansion easy ; also, " toaster " Compact Macs did not have easily accessible hard drive bays ( or, in the case of the Mac Plus, any hard drive bay at all ), so on those models, external SCSI disks were the only reasonable option.

Every hyperbola is congruent to the origin-centered East-West opening hyperbola sharing its same eccentricity ε ( its shape, or degree of " spread "), and is also congruent to the origin-centered North-South opening hyperbola with identical eccentricity ε — that is, it can be rotated so that it opens in the desired direction and can be translated ( rigidly moved in the plane ) so that it is centered at the origin.

Every day most Jains bow and say their universal prayer, the Navakar Mantra which is also known variously as Panch Parmesthi Sutra, Panch Namaskar Sutra.

Every subfield of an ordered field is also an ordered field in the inherited order.

Every subfield of an ordered field is also an ordered field ( inheriting the induced ordering ).

The band also contributed a rendition of " Ain't That Pretty At All " to the Warren Zevon tribute album Enjoy Every Sandwich.

Every synod elects a Permanent Judicial Commission, which has original jurisdiction in remedial cases brought against its constituent presbyteries, and which also serves as an ecclesiastical court of appeal for decisions rendered by its presbyteries ' Permanent Judicial Commissions.

Every RFC is submitted as plain ASCII text and is published in that form, but may also be available in other formats.

Good Trouble ( 1982 ) and Wheels Are Turnin ' ( 1984 ) were follow-up albums which also did well commercially, the former containing the hit singles " Keep the Fire Burnin '" ( U. S. # 7 ), " Sweet Time " ( U. S. # 26 ) and the un-ranked " The Key " and the latter containing the # 1 hit single " Can't Fight This Feeling " plus three more hits: " I Do ' Wanna Know " ( U. S. # 29 ), " One Lonely Night " ( U. S. # 19 ), " Live Every Moment " ( U. S. # 34 ) and the un-ranked " Break His Spell ".

Every republic of the Soviet Union also was awarded with the Order of Lenin.

Every Economic union and Economic and monetary union has also a Common market

Every time I think of a joke, I ’ m also telling myself a new joke.

The last two lines of the Act IV-scene 2 funeral song may also have inspired the lines W. H. Auden, the librettist for Stravinsky's The Rake's Progress, puts into the mouth of Anne Truelove at the end of the opera: " Every wearied body must late or soon return to dust ".

< li > Every positive definite matrix is invertible and its inverse is also positive definite.

Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G

: Every integer which can be written as the sum of two primes, can also be written as the sum of as many primes as one wishes, until all terms are units.

Every human advance solves one problem but also engenders another.