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Page "Equivalence relation" ¶ 87
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Hence and three
Hence it has three main elements: description of the phenomena ; developing a general theory about the causes of various types of change ; and applying those theories to specific facts.
Hence, three additional forms for ubiquitous systems have been proposed:
Hence these three criteria:
Hence, William Hallowes Miller in 1839 was able to give each face a unique label of three small integers, the Miller indices which are still used today for identifying crystal faces.
Hence, it has three interlocking reproductive strategies: dominance of local habitats by clonal growth, survival of long inhospitable periods with buried seeds, and dispersal to new sites with wind-dispersed seeds.
" Hence most of the prosimians and platyrrhines have three premolars.
Hence the new set of order parameters describing the three magnetic phases consists of both and.
Sfumato is where there are no harsh outlines, and it is painted with full strokes that enhance color and light. The areas blend together Hence the term " Sfumato " was used by Michael J. Gelb on his book How to Think Like Leonardo da Vinci to describe one of da Vinci's mental abilities, namely the ability to hold three paradoxical ideas in one's mind without difficulty.
Hence in its current form the name combines three forms of the word hill.
Hence there are 57 rotationally distinct colourings of the faces of a cube in three colours.
Hence, managing the surgical reconstruction of a damaged, defective, or deformed nose, requires that the plastic surgeon manipulate three ( 3 ) anatomic layers:
" Hence, the Saṃdhinirmocana Sūtra, as the doctrinal trailblazer of Yogācāra, inaugurated the paradigm of the three turnings of the wheel of Dharma, with its own tenets in the " third turning ".
Hence, the main forces were formed in three armies for the advance towards Skopje, while a division and an independent brigade were to cooperate with the Montenegrins in the Sanjak of Novi Pazar.
Hence, all three radical axes pass through the same point, the radical center.
Hence the three Euler Angles can be calculated.
Hence, the irradiance E < sub > tilt </ sub > on a tilted plane consists of three components: E < sub > tilt </ sub > = E < sub > dir </ sub > + E < sub > dif </ sub > + E < sub > ref </ sub >.
Hence, the half-life is bimodal, with peaks at one and three hours in the US population.
Hence, three additional forms for ubiquitous systems have been proposed:.
# Hence I am called Hermes Trismegist, having the three parts of the philosophy of the whole world.
Hence the characteristic, calculus ratiocinator, and encyclopedia form three pillars of Leibniz's project.
Hence for purposes of determining stratification, a function is three types higher than the members of its field.
Hence, an infantry brigade could consist of three battalions of infantry, but a cavalry brigade of equivalent size would have three regiments.

Hence and defining
Hence, according to the New Testament principle, for women not to be permitted to speak in the church meetings means that women are not permitted to teach with authority in relation to the defining of doctrine.

Hence and properties
Hence it is the atomic number alone that determines the chemical properties of an element ; and it is for this reason that an element can be defined as consisting of any mixture of atoms with a given atomic number.
Hence his wife and sons were allowed to inherit his lands and properties ; Hastings himself was buried in St George's Chapel, Windsor, next to Edward IV.
Hence there is only one phase, and it has the physical properties of a dense gas, but is also referred to as a supercritical fluid.
Hence, the Upper Room building and other surrounding properties were placed up for sale.
Hence Tarski's theorem is much easier to motivate and prove than the more celebrated theorems of Gödel about the metamathematical properties of first-order arithmetic.
Hence, a split was agreed upon, with Jolly Blackburn leaving with the rights to Knights of the Dinner Table and a few other properties.
Hence, it is generally possible to define a sedimentation coefficient that depends only on the properties of the particle and the surrounding fluid.
Hence a modal may introduce a chain ( technically catena ) of verb forms, in which the other auxiliaries express properties such as aspect and voice, as in He must have been given a new job.
Hence, if a thing has n properties, each of them — if on the same level of abstraction — is proportionally worth n < sup >- 1 </ sup >.
Hence, some sliding mode observers have attractive properties similar to the Kalman filter but with simpler implementation.
Hence several imposing properties exist in the village such as Shanghai house, Santa Cruz and Sydney house.
Hence properties soar to exorbitant prices, making it more and more difficult for entry level income earners to afford to live there.
Hence this oil has to be periodically tested to ascertain its basic electrical properties, make sure it is suitable for further use, and ascertain the need for maintenance activities like filtration / regeneration.

Hence and equivalence
Hence it is difficult to conceive of a packing of the atoms in this material in which the oxygen atoms are far from geometrical equivalence.
Hence permutation groups ( also known as transformation groups ) and the related notion of orbit shed light on the mathematical structure of equivalence relations.
Hence an equivalence relation is a relation that is Euclidean and reflexive.
Hence to express the remainder we would have to write, rather than, since equivalence can only be said of common residues with the same sign.
" Hence an argument which claimed that the two parties could be viewed as " equally " culpable in a struggle for supremacy, would be advocating " moral equivalence.
Hence thermal equilibrium between systems is an equivalence relation, and this is the substance of the zeroth law of thermodynamics.
Hence, given the information that the identity functors form an equivalence of categories, in this example one still can choose between two natural isomorphisms for each direction.
In particular, if A is a sentence of arithmetic then True ( g ( A )) holds in N if and only if A is true in N. Hence for all A, the Tarski T-sentence True ( g ( A )) ↔ A is true in N. But the diagonal lemma yields a counterexample to this equivalence, by giving a " Liar " sentence S such that S ↔ ¬ True ( g ( S )) holds.
Hence given Planck units, the mass-energy equivalence E = mc² simplifies to E = m, so that the Planck energy and mass are numerically identical.

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