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Page "Internal set theory" ¶ 20
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Every and classical
Every argues that " the disparagement of myth in our own civilization " stems partly from objections to perceived idolatry, objections which intensified in the Reformation, both among Protestants and among Catholics reacting against the classical mythology revived during the Renaissance.
Every year he exhibited work of one class or another: occasionally a public monument in the round, like those of Pasquale Paoli ( 1798 ) or Captain Montague ( 1802 ) for Westminster Abbey, of Sir William Jones for University College, Oxford ( 1797 – 1801 ), of Nelson or Howe for St Paul's Cathedral ; more often memorials for churches, with symbolic Acts of Mercy or illustrations of Scripture texts, both commonly in low relief ( 1801 ), Miss Cromwell, Chichester ( 1800 ), Mrs Knight, Milton, Cambridge ( 1802 ), and many more ; and these pious labours he would vary from time to time with a classical piece like those of his earliest predilection.
Every single step in classical ballet is performed with hips, knees and feet as turned out as possible, except when otherwise specified by choreography.
Every formula in classical logic is equivalent to a formula in prenex normal form.
Every first-order formula is logically equivalent ( in classical logic ) to some formula in prenex normal form.
Every autumn, according to Plutarch ( Life of Lycurgus, 28, 3 – 7 ), the Spartan ephors ( classical Greek ) would pro forma declare war on the helot population so that any Spartan citizen could kill a helot without fear of blood guilt.
Every summer, it hosts an international classical music festival.

Every and theorem
** Well-ordering theorem: Every set can be well-ordered.
* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
* Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ".
* Every pair of congruence relations for an unknown integer x, of the form x ≡ k ( mod a ) and x ≡ l ( mod b ), has a solution, as stated by the Chinese remainder theorem ; in fact the solutions are described by a single congruence relation modulo ab.
Cantor points out that his constructions prove more — namely, they provide a new proof of Liouville's theorem: Every interval contains infinitely many transcendental numbers.
In cybernetics, the Good Regulator or Conant-Ashby theorem is stated " Every Good Regulator of a system must be a model of that system ".
Every Tychonoff cube is compact Hausdorff as a consequence of Tychonoff's theorem.
* Krull's theorem ( 1929 ): Every ring with a multiplicative identity has a maximal ideal.
Every proper rotation is the composition of two reflections, a special case of the Cartan – Dieudonné theorem.
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 Hermitian matrix is a normal matrix, and the finite-dimensional spectral theorem applies.
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 Boolean algebra can be obtained in this way from a suitable topological space: see Stone's representation theorem for Boolean algebras.
Every theorem proved with idealistic methods presents a challenge: to find a constructive version, and to give it a constructive proof.
Every group of prime order is cyclic, since Lagrange's theorem implies that the cyclic subgroup generated by
For example, to study the theoremEvery bounded sequence of real numbers has a supremum ” it is necessary to use a base system which can speak of real numbers and sequences of real numbers.
# Every K3 surface is Kähler ( by a theorem of Y .- T. Siu ).
* Every finite-dimensional simple algebra over R must be a matrix ring over R, C, or H. Every central simple algebra over R must be a matrix ring over R or H. These results follow from the Frobenius theorem.
* Every automorphism of a central simple algebra is an inner automorphism ( follows from Skolem – Noether theorem ).
* Conway's cosmological theorem: Every sequence eventually splits into a sequence of " atomic elements ", which are finite subsequences that never again interact with their neighbors.
Every comparability graph is perfect: this is essentially just Mirsky's theorem, restated in graph-theoretic terms.
Every rotation in three dimensions is defined by its axis — a direction that is left fixed by the rotation — and its angle — the amount of rotation about that axis ( Euler rotation theorem ).
* Moise's theoremEvery 3-manifold has a triangulation, unique up to common subdivision

Every and applies
The 1872 Parks Regulation Act created positions of " park keeper " and also provided that " Every police constable belonging to the police force of the district in which any park, garden, or possession to which this Act applies is situate shall have the powers, privileges, and immunities of a park-keeper within such park, garden, or possession.
Every Cardinal of the Roman Catholic Church is still called a Prince of the Church because their College of Cardinals elects a new pope ( de facto from their number ) during a period sede vacante in a special session called a conclave, where an age-limit applies.

Every and natural
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 group G acts on G, i. e. in two natural but essentially different ways:, or.
Every man-made product is composed of natural resources ( at its fundamental level ).
* natural language — Every good boy deserves fruit ; and
Every smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces:
Every twin prime pair except ( 3, 5 ) is of the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception of < var > n </ var > = 1, < var > n </ var > must end in 0, 2, 3, 5, 7, or 8.
Every natural hollow is full of water, around the margin of which, long grasses, reeds and other aquatic plants grow in the greatest profusion, often making it difficult to say where the land ends and the water begins.
Every topological ring is a topological group ( with respect to addition ) and hence a uniform space in a natural manner.
Every smooth manifold defined in this way has a natural diffeology, for which the plots correspond to the smooth maps from open subsets of R < sup > n </ sup > to the manifold.
* Every natural number a has a successor, denoted by Sa.
Every step of the process is natural and healthy, it is only when a person gets stuck in one step for a long period of time then the grieving can become unhealthy, destructive and even dangerous.
* Every number of the form 2 < sup > m </ sup > p for a natural number m and a prime number p such that p < 2 < sup > m + 1 </ sup > is also semiperfect.
* Every finite or cofinite subset of the natural numbers is computable.
Every minimal pair of natural numbers has and, for otherwise the pair would belong to and be at least as small in both coordinates, contradicting the assumption that is minimal.
Every finite ordinal ( natural number ) is initial, but most infinite ordinals are not initial.
Every year Plum Creek replants approximately 85 million seedlings and plans for the natural regeneration of millions of trees.
Every infinitely divisible probability distribution corresponds in a natural way to a Lévy process, i. e., a stochastic process
Every C *- algebra has an approximate identity of positive elements of norm ≤ 1 ; indeed, the net of all positive elements of norm ≤ 1 ; in A with its natural order always suffices.
* Every individual will have a responsibility to contribute back to the greater natural and social community from his / her Brown School experience.
These rights are guaranteed to " Every individual ," that is, every natural person.
Every aspect of the ecosystem from the different species of plants to the diversity of animal species contributes to natural services like water purification, provision of food, fuel, fiber, and biochemicals, nutrient cycling, pollination and seed dispersal, and climate regulation, just to name a few.
Every August it is held the " Strawberry Festival " where the producers exhibit their natural production or their by-products elaborated from the fruit.
Every year two or more junior Bachelors of Arts students who had made the greatest progress in mathematics and natural philosophy were to be awarded a prize from the fund.

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