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Every and second-order For example, second-order arithmetic can express the principle " Every countable vector space has a basis " but it cannot express the principle " Every vector space has a basis ". Many principles that imply the axiom of choice in their general form ( such as " Every vector space has a basis ") become provable in weak subsystems of second-order arithmetic when they are restricted. * ( Soundness ) Every provable second-order sentence is universally valid, i. e., true in all domains under standard semantics. * ( Completeness ) Every universally valid second-order formula, under standard semantics, is provable. Every second-order linear ODE on the extended complex plane with at most four regular singular points, such as the Lamé equation or the hypergeometric differential equation, can be transformed into this equation by a change of variable.

Every and linear Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable. Every time a diode switches from on to off or vice versa, the configuration of the linear network changes. Every vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism. Every smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces: * Every linear combination of its components Y = a < sub > 1 </ sub > X < sub > 1 </ sub > + … + a < sub > k </ sub > X < sub > k </ sub > is normally distributed. Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors. Every sedenion is a real linear combination of the unit sedenions 1, < var > e </ var >< sub > 1 </ sub >, < var > e </ var >< sub > 2 </ sub >, < var > e </ var >< sub > 3 </ sub >, ..., and < var > e </ var >< sub > 15 </ sub >, Every octonion is a real linear combination of the unit octonions: Every physical quantity has a Hermitian linear operator associated to it, and the states where the value of this physical quantity is definite are the eigenstates of this linear operator. Every vector in the space may be written as a linear combination of unit vectors. Every nontrivial proper rotation in 3 dimensions fixes a unique 1-dimensional linear subspace of R < sup > 3 </ sup > which is called the axis of rotation ( this is Euler's rotation theorem ). Every finite-dimensional normed space is reflexive, simply because in this case, the space, its dual and bidual all have the same linear dimension, hence the linear injection J from the definition is bijective, by the rank-nullity theorem. Every finite-dimensional Hausdorff topological vector space is reflexive, because J is bijective by linear algebra, and because there is a unique Hausdorff vector space topology on a finite dimensional vector space. Every real m-by-n matrix yields a linear map from R < sup > n </ sup > to R < sup > m </ sup >. * Every ( biregular ) algebraic automorphism of a projective space is projective linear. Every bounded linear transformation from a normed vector space to a complete, normed vector space can be uniquely extended to a bounded linear transformation from the completion of to. Every vector a in three dimensions is a linear combination of the standard basis vectors i, j, and k. Every lattice in can be generated from a basis for the vector space by forming all linear combinations with integer coefficients. Every linear program has a dual problem with the same optimal solution, but the variables in the dual problem correspond to constraints in the primal problem and vice versa. * Every irreducible polynomial in K which has a root in L factors into linear factors in L. Every linear function on a finite-dimensional space is continuous.

Every and with Every time I closed my eyes, I saw Gray Eyes rushing at me with a knife. 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 Wednesday night through Oct. 11 there will be an elaborate colored fountain display, with 229 nozzles throwing jets of water up to 130 feet. Every doll in the house must be going with her ''. ** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion. Every unit of length has a corresponding unit of area, namely the area of a square with the given side length. * Revised Code of Washington 9. 12. 010: " Every person who brings on his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of this state, with intent thereby to distress or harass a defendant in the suit, or who serves or sends any paper or document purporting to be or resembling a judicial process, that is not in fact a judicial process, is guilty of a misdemeanor ; and in case the person offending is an attorney, he or she may, in addition thereto be disbarred from practicing law within this state. Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra. 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 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 unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions. * Every commutative real unital Noetherian Banach algebra with no zero divisors is isomorphic to the real or complex numbers. Every cladogram is based on a particular dataset that was analyzed with a particular method. Every city expansion would imply a new circle ( canals together with town walls ). Jimmy Hatlo's They'll Do It Every Time was often displayed in a two-panel format with the first panel showing some deceptive, pretentious, unwitting or scheming human behavior and the second panel revealing the truth of the situation. Every year, the European Joint Conferences on Theory and Practice of Software ( ETAPS ) sponsors the International Conference on Compiler Construction ( CC ), with papers from both the academic and industrial sectors. Every play is subject to booth review with coaches only having one challenge. According to Every, one example may be " the myth of St. George " and other stories about saints battling dragons, which were " modelled no doubt in many cases on older representations of the creator and preserver of the world in combat with chaos ". * Every three years since Earnhardt's death, someone associated with Earnhardt has won the Daytona 500 ( his son Dale Earnhardt, Jr. in 2004, Earnhardt's replacement Cup driver Kevin Harvick in 2007, and Earnhardt Ganassi's Jamie McMurray in 2010. Every song they wrote was written with an eye toward giving it " deep hidden meaning " or D. H. M. In Norse mythology, Draupnir ( Old Norse " the dripper ") is a gold ring possessed by the god Odin with the ability to multiply itself: Every ninth night eight new rings ' drip ' from Draupnir, each one of the same size and weight as the original. Every system must have a class designated as " root ", with one of its creation procedures designated as " root procedure ". Every year, hundreds of new titles are published in Esperanto along with music.

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