# Finite Sentence Examples

Apart from God, the

**finite**being has no reality, and we only have the idea of it from God.Diogenes distinctly taught that the world is of

**finite**duration, and will be renewed out of the primitive substance.The invariant theory then existing was classified by them as appertaining to "

**finite**continuous groups."God is not fully comprehensible by us, says Albert, because the

**finite**is not able to grasp the infinite, yet he is not altogether beyond our knowledge; our intellects are touched by a ray of his light, and through this contact we are brought into communion with him.Here also it can be seen that the science of the

**finite**ordinals is a particular subdivision of the general theory of classes and relations.The name lemniscate is sometimes given to any crunodal quartic curve having only one real

**finite**branch which is symmetric about the axis.To Lagrange, perhaps more than to any other, the theory of differential equations is indebted for its position as a science, rather than a collection of ingenious artifices for the solution of particular problems. To the calculus of

**finite**differences he contributed the beautiful formula of interpolation which bears his name; although substantially the same result seems to have been previously obtained by Euler.The one is a problem of interpolation, the other a step towards the solution of an equation in

**finite**differences.He was also the first to consider the difficult problems involved in equations of mixed differences, and to prove that an equation in

**finite**differences of the first degree and the second order might always be converted into a continued fraction.There is a

**finite**number of baseballs, beanbags, and balloons.AdvertisementPain and sin must have been reduced to a minimum by God; though they are so ingrained in the

**finite**that we have to make up our minds even to the endless sin and endless punishments of hell.They are infinite and perfect when the En Soph imparts his fullness to them, and

**finite**and imperfect when that fullness is withdrawn from them.One or more of the electrons may be detached from the system by a

**finite**force, the number so detachable depending on the valency of the atom; if the atom loses an electron, it becomes positively electrified; if it receives additional electrons, it is negatively electrified.A perfectly formless matter (materia prima) was regarded by him as the universal substratum and common element of all

**finite**existences.It is, moreover, the Good, in so far as all

**finite**things have their purpose in it, and ought to flow back to it.AdvertisementBut the Fichtean teaching appeared on the one hand to identify too closely the ultimate ground of the universe of rational conception with the

**finite**, individual spirit, and on the other hand to endanger the reality of the world of nature by regarding it too much after the fashion of subjective idealism, as mere moment, though necessitated, in the existence of the**finite**thinking mind.We find Philo Judaeus endeavouring to free the concept of the Old Testament Yahweh from anthropomorphic characteristics and

**finite**determinations.We proceed to sketch the theory of the

**finite**displacements of a rigid body.God is not

**finite**, not sinful, etc.Thus log x is the integral function of 1/x, and it can be shown that log x is a genuinely new transcendent, not expressible in

**finite**terms by means of functions such as algebraical or circular functions.AdvertisementExternal things are produced by the will of the divine intelligence; they are caused, and caused in a regular order; there exists in the divine mind archetypes, of which sense experience may be said to be the realization in our

**finite**minds.The relation between the divine mind and

**finite**intelligence, at first thought as that of agent and recipient, is complicated and obscure when the necessity for explaining the permanence of real things comes forward.This apparent motion is due to the

**finite**velocity of light, and the progressive motion of the observer with the earth, as it performs its yearly course about the sun.The limitation of power is introduced as in all optical instruments, by the finiteness of the length of a wave of light which causes the image of an indefinitely narrow slit to spread out over a

**finite**width in the focal plane of the observing telescope.Thus if a molecule were set into vibration at a specified time and oscillated according to the above equation during a

**finite**period, it would not send out homogeneous vibrations.AdvertisementHaving, however, in consequence, lost his professorship at Jena, he gradually altered his views, until at length he decided that God is not mere moral order, but also reason and will, yet without consciousness and personality; that not mankind but God is the absolute; that we are only its direct manifestations, free but

**finite**spirits destined by God to posit in ourselves Nature as the material of duty, but blessed when we relapse into the absolute; that Nature, therefore, is the direct manifestation of man, and only the indirect manifestation of God; and, finally, that being is the divine idea or life, which is the reality behind appearances.But in a philosophy which reduces everything to phenomenal appearance except the self-interacting substance of God, there is no room for either the bodies or the souls of

**finite**substances or human persons.Bradley, however, having satisfied himself, like Spinoza, by an abuse of the word " independent," that " the

**finite**is self-discrepant," goes on to ask what the one Real, the absolute, is; and, as he passed from Herbart to Spinoza, so now he passes from Spinoza to Kant.Calderwood, in his Philosophy of the Infinite (1854), made the pertinent objection that, though thought, conception and knowledge are

**finite**, the object of thought may be infinite.Hamilton, in fact, made the double mistake of limiting knowledge to what we can conceive, and confusing the determinate with the

**finite**or limited.Further, to allow of a correction being applied for the

**finite**length of the magnets the whole series of settings is repeated with the centre of the deflecting magnet at 40 cm.Unlike the Hindu, Xenophanes inclined to pantheism as a protest against the anthropomorphic polytheism of the time, which seemed to him improperly to exalt one of the many modes of

**finite**existence into the place of the Infinite.Like Hamilton, Mansel maintained the purely formal character of logic, the duality of consciousness as testifying to both self and the external world, and the limitation of knowledge to the

**finite**and "conditioned."This is, however, an application of categories from a field where the conditions are

**finite**to a sphere in which the circumstances are infinite."This is the moment of the

**finite**.The completeness and self-consistency which our ideal requires can be realized only in a form of being in which subject and object, will and desire, no longer stand as exclusive opposites, from which it seemed at once to follow that the

**finite**self could not be a reality nor the infinite reality a self.Thus we distinguish in the divine system beginning, middle and end; but these three are in essence one - the difference is only the consequence of our

**finite**comprehension.No

**finite**predicates can be applied to him; his mode of being cannot be determined by any category.The Mosaic account, then, is to be looked upon merely as a mode in which is faintly shadowed forth what is above

**finite**comprehension.Their speculation as to the nature of God had led them gradually to separate him by an infinite distance from all creation, and to feel keenly the opposition of the

**finite**and the infinite, the perfect and the imperfect, the eternal and the temporal.Unlike Thales, he was struck by the infinite variety in things; he felt that all differences are

**finite**, that they have emerged from primal unity (first called epxn by him) into which they must ultimately return, that the Infinite One has been, is, and always will be, the same, indeterminate but immutable.The composition of

**finite**rotations about parallel axes is, a particular case of the preceding; the radius of the sphere is now infinite, and the triangles are plane.For this purpose the infinitesimal displacements of W the various joints are replaced by

**finite**lengths proportional to them, and there- FIG.This means that, if the material of the frame were absolutely unyielding, no

**finite**stresses in the bars would enable it to withstand the extraneous forces.In the case of a chain hanging freely under gravity it is usually convenient to formulate the conditions of equilibrium of a

**finite**portion PQ.For purposes of mathematical treatment a force which produces a

**finite**change of velocity in a time too short to be appreciated is regarded as infinitely great, and the time of action as infinitely short.The effect of ordinary

**finite**forces during the infinitely short duraticm of this impulse is of course ignored.The total impulse in any

**finite**interval of time is the integral of the impulses corresponding to the infinitesimal elements 3t into which the interval may be subdivided; the summation of which the integral is the limit is of course to be understood in the vectorial sense.The question presents itself whether ther then is any other law of force, giving a

**finite**velocity from infinity, under which all**finite**orbits are necessarily closed curves.If, on the other hand, the body is

**finite**, certain terminal conditions have to be satisfied.In order to allow for the

**finite**stiffness and strength of materials, the least distance of the centre of resistance inward from the nearest edge of the joint is made to bear a definite proportion to the depth of the joint measured in the same direction, which proportion is fixed, sometimes empirically, sometimes by theoretical deduction from the laws of the strength of materials.The essence of God, for instance, he held to be love; God, he said, can love nothing inferior to himself; but he cannot be an object of love to himself without going out, so to speak, of himself, without manifesting his infinity in a

**finite**form; in other words, by becoming man.These effects, as Hertz showed, indicated the establishment of stationary electric waves in space and the propagation of electric and magnetic force through space with a

**finite**velocity.Cudworth's ideas, like Plato's, have "a constant and never-failing entity of their own," such as we see in geometrical figures; but, unlike Plato's, they exist in the mind of God, whence they are communicated to

**finite**understandings.He holds that we are rationally justified in affirming human immortality and the existence of a

**finite**God who is to be a constitutional ruler, but not a despot, over the souls of men.The histories of philosophy may quite correctly describe his theory as the logical development of Descartes's doctrines of the one Infinite and the two

**finite**substances, but Spinoza himself was never a Cartesian.The foundation of the system is the doctrine of one infinite substance, of which all

**finite**existences are modes or limitations (modes of thought or modes of extension).Bostrom's philosophy is logically expressed and based on the one great conception of a spiritual, eternal, immutable Being, whose existence is absolute, above and external to the

**finite**world of time and space.In the mathematical sense, however, this selection is arbitrary; the reproduction of a

**finite**object with a**finite**aperture entails, in all probability, an infinite number of aberrations.This number is only

**finite**if the object and aperture are assumed to be " infinitely small of a certain order"; and with each order of infinite smallness, i.e.The existence of an optical system, which reproduces absolutely a

**finite**plane on another with pencils of**finite**aperture, is doubtful; but practical systems solve this problem with an accuracy which mostly suffices for the special purpose of each species of instrument.The cycle of its transformations and successive condensations constitutes the life of the universe, the mode of existence proper to

**finite**and particular being.We may investigate the forces which act between

**finite**portions of a liquid in the same way as we investigate the forces which act between**finite**portions of a solid.The first part establishes the laws of the elasticity of a

**finite**portion of the solid subjected to a homogeneous strain, and deduces from these laws the equations of the equilibrium and motion of a body subjected to any forces and displacements.The second part endeavours to deduce the facts of the elasticity of a

**finite**portion of the substance from hypotheses as to the motion of its constituent molecules and the forces acting between them.Laplace assumed that the liquid has uniform density, and that the attraction of its molecules extends to a

**finite**though insensible distance.Integrating the first term within brackets by parts, it becomes - fo de Remembering that 0(o) is a

**finite**quantity, and that Viz = - (z), we find T = 4 7rp f a, /.(z)dz (27) When c is greater than e this is equivalent to 2H in the equation of Laplace.Since the circumference of a circle is proportional to its radius, it follows that if the ratio of the radii be commensurable, the curve will consist of a

**finite**number of cusps, and ultimately return into itself.In such a case the two systems must be regarded as a single more complex one, the absorbed vibration becomes large, though remaining always

**finite**, and the transmitted vibration undergoes a remarkable change in its period.From the basis of immediate experience or perception thought proceeds by comparison and abstraction, establishing connexions among facts, but remaining in its nature mediate and

**finite**.It is impossible that there should be a God, for if so he would of necessity be

**finite**.But a

**finite**God, a God that is known, is no God.But I distinguish the two

**finite**causes self and not-self Panther ism.They are not mere modifications of this cause or properties, as with Spinoza, - they are free forces having their power or spring of action in themselves, and this is sufficient for our idea of independent

**finite**reality.This is the third and highest stage of development, the relation of the

**finite**and the infinite.The East typifies the infinite, Greece the

**finite**or reflective epoch, the modern era the stage of relation or correlation of infinite and**finite**.Y g Y g infinite or causes, correlative and reciprocally

**finite**, to which absolute.The correlation of the ideas of infinite and

**finite**does not necessarily imply their correality, as Cousin supposes; on the contrary, it is a presumption that**finite**is simply positive and infinite negative of the same - that the**finite**and infinite are simply contradictory relatives.The answer to this is that in the case of contradictory statements - A and not A - the latter is a mere negation of the former, and posits nothing; and the negation of a notion with positive attributes, as the

**finite**, does not extend beyond abolishing the given attributes as an object of thought.This is a mere paralogism; we can never infer either absolute or infinite from relative or

**finite**.It is, moreover, to be noticed that the points at infinity may be all or any of them imaginary, and that the points of intersection, whether

**finite**or at infinity, real or imaginary, may coincide two or more of them together, and have to be counted accordingly; to support the theorem in its universality, it is necessary to take account of these various circumstances.Both Plato and Aristotle devoted much thought to the discussion as to which is most truly real, the

**finite**objects of sense, or the universal idea of each thing laid up in the mind of God; what is the nature of that unity which lies behind the multiplicity and difference of perceived objects ?A similar relation exists in thought between the various grades of species and genera; the highest genus is the " infinitely infinite," each subordinated genus being infinite in relation to the particulars which it denotes, and

**finite**when regarded as a unit in a higher genus.If human understanding cannot fully solve the infinite problem of the universe, man may at least see that at no stage of his

**finite**experience is he necessarily the sport of chance, and that he can practically secure his own wellbeing.We find ourselves, when we try, compelled to lose our positive ideas of

**finite**spaces in the negative idea of Immensity or Boundlessness, and our positive ideas of**finite**times in the negative thought of Endlessness.Anything, as far as " constant observation " tells us, might a priori have been the natural cause of anything; and no

**finite**number of " observed " sequences, per se, can guarantee universality and necessity.For " our perceptions of the particular existence of

**finite**beings without us " go beyond mere probability, yet they are not purely rational.As to extent, it may be said, in a general way, that while no definite limits can be set to the possible extent of the universe, or the distance of its farthest bodies, it seems probable, for reasons which will be given under Star, that the system to which the stars that we see belong, is of

**finite**extent.The divine omnipotence is quantitatively represented by the sum of the forces of nature, and qualitatively distinguished from them only as the unity of infinite causality from the multiplicity of its

**finite**phenomena.In his earlier days he called it a feeling or intuition of the universe, consciousness of the unity of reason and nature, of the infinite and the eternal within the

**finite**and the temporal.The specific feature of Christianity is its mediatorial element, its profound feeling of the striving of the

**finite**individual to reach the unity of the infinite whole, and its conception of the way in which Deity deals with this effort by mediatorial agencies, which are both divine and human.But an infinite distance (which Zeno fails to distinguish from a

**finite**distance infinitely divided) cannot be traversed in a**finite**time.The "infinity" of the premise is an infinity of subdivisions of a distance which is

**finite**; the "infinity" of the conclusion is an infinity of distance.Thus Zeno again confounds a

**finite**distance infinitely divided with an infinite distance.Lord Rayleigh has pointed out that all theories are defective in that they disregard the fact that one at least of the media is dispersive, and that it is probable that

**finite**reflection would result at the interface of media of different dispersive powers, even in the case of waves for which the refractive indices are absolutely the same.Religious thinkers are faced by the problem of the Creator and the created, and the necessity for formulating a close relationship between God and man, the Infinite and Perfect with the

**finite**and imperfect.In support of such a view are adduced not only the metaphysical difficulty of postulating any relationship between the infinite and the purely

**finite**, but also the ethical 1 P. G., tom.Daub in his Judas Ishcarioth argued that a

**finite**evil presupposes an absolute evil, and the absolute evil as real must be in a person.The central projection, of which the centre is the middle point of the entrance pupil on the plane focused for, will show in weaker systems, or those very much stopped down, a certain

**finite**depth of definition; that is to say, the totality of points, which lie out of the plane focused for, and which are projected with circles of confusion so small that they appear to the eye as sharp points, will include the sharp object relief, and determine the depth of definition of the lens.For

**finite**intelligences there was an inevitable incompleteness so far as knowledge of matters of fact was concerned.It was conjectured that this number is normal, meaning that it contains all

**finite**bit strings.Apply the algebra of

**finite**automata to design systems and to solve simple problems on creating acceptors for particular languages.It is called algebraic Curves over a

**Finite**Field and is currently 644 pages.These are automatically computed by

**finite**difference approximation (either forward or central differences ).Necessary algorithmic problems are then solved by converting types to

**finite**tree automata.The maximum number of states that the

**finite**automaton requires is set by default to 500.The

**finite**scheme of things, to use a homely phrase, is thus actually lifting itself by its own bootstraps.Furthermore, they can replace heavy 3D numerical calculations (for example

**finite**element calculations) with high accuracy.Kolmogorov's proposal outlined strives for the firmer and less contentious ground expressed in

**finite**combinatorics and effective computation.To a considerable extent,

**finite**and infinite combinatorics are parts of the same subject.A group whose commutator factor group is

**finite**can only have**finite**nilpotent quotient groups.They therefore represent a

**finite**scientific and economic resource and are a notable determinant of landscape character.You will be helping to alleviate human famine by taking less out of the World's

**finite**resources.Microscopically, however, quantal effects of the large, yet

**finite**, ensemble of strongly interacting fermions need to be considered.Furthermore, it is not possible for the infinite and

**finite**and**finite**to mix, making an infinite**finite**.The interpretation we produced was itself either

**finite**or denumerably infinite.Since only

**finite**regions are considered, the algebras are called local algebras.It should be remembered that titles and rhythm descriptions for such pieces are not always

**finite**.Although electricity travels fast, its speed is still

**finite**and over a wire it is slower than in a vacuum.For them, the realities of a very

**finite**planet simply do not equate with their conventional wisdoms of infinite growth.Indeed, we only have a sense of the infinite, or what is not

**finite**, or what is not**finite**, from various created**finite**viewpoints.As speculative computations may be infinite, while mandatory ones remain

**finite**, while mandatory ones remain**finite**, divergence should be defined with the greatest care.A universe with nonzero size and

**finite**energy density appears from a quantum fuzz.He warns hoteliers that there is probably a

**finite**window for charging.Hence, the input impulse response will consist of a series of pulses of

**finite**width.Also, since all operations are performed with

**finite**precision, the results are of limited precision and necessarily inexact.For Aristotle all the elements in an actual

**finite**exist simultaneously, whereas a potential infinite is realized over time by addition or division.The question is if G-d's knowledge is infinite, how can something infinite be placed in something

**finite**, the written torah.The

**finite**nature of the human mind cannot grasp and comprehend the infinite.It is beyond

**finite**minds to understand the infinite.The effect of

**finite**efficiency for the quantum interrogation is delineated for the various schemes.Invariant Theory of

**Finite**Groups This introductory lecture will be concerned with polynomial invariant Theory of**Finite**Groups This introductory lecture will be concerned with polynomial invariants of**finite**groups which come from a linear group action.These are usually called ' closed universes ' and they have a

**finite**total lifetime.To produce a

**finite**straight line continuously in a straight line.In fact GAP supports

**finite**fields with elements represented via discrete logarithms only up to a given size.A

**finite**group G is called monomial (or M -group) if each ordinary irreducible character of G is monomial.But it can lead to the more efficient use of our

**finite**natural resources.You are a

**finite**concept that represents the negation of your own infinite essence.Current astronomical observations can't really tell us whether the world really did have an infinite past or just a

**finite**one.Since there is an infinite ordinal, every

**finite**ordinal is a set and the first infinite ordinal ω is a set.The size evolution of polytetrahedral packings enables us to study the development of bulk liquid structure in

**finite**systems.The ChemShell QM/MM procedures are most commonly with

**finite**clusters, especially for highly polar materials where cutoffs cannot be used.Or are they actually not infinitely precise, given the practical limitations of measuring them with a

**finite**universe?We present a statistical

**finite**state model that combines prosodic, linguistic and punctuation class features.At a stroke MVNO could remove the absolute barrier to entry arising from the

**finite**available radio spectrum.**Finite**generalized tetrahedron groups with a cubic relator 2003/21 Vincent Schmitt.In order to make such models tractable, we require that they have

**finite**domains.Such tentative evidence is not yet sufficiently weighty to change the author's convictions that the universe must be

**finite**in all respects.We have 62=W12+W22+032=P2 (N) 2 Y 2+P2 (A I - 3) 2 If AN, AD be both

**finite**, we learn from (7) that there is no direction perpendicular to the primary (polarized) ray in which the secondary light vanishes.So long as the particles are small no such vanishing of light in oblique directions is observed, and we are thus led to the conclusion that the hypothesis of a

**finite**AN and of vibrations in the plane of polarization cannot be reconciled with the facts.Special experiments were made to determine the work done against resistances outside the vessel of water, which amounted to about 006 of the whole, and corrections were made for the loss of heat by radiation, the buoyancy of the air affecting the descending weights, and the energy dissipated when the weights struck the floor with a

**finite**velocity.The reason why the whole of the energy of the current is not available is that heat must always be generated in a wire in which a

**finite**current is flowing, so that, in the case of a battery in which the whole of the energy of chemical affinity is employed in producing a current, the availability of the energy is limited only on account of the resistance of the conductors, and may be increased by diminishing this resistance.If the principle of the universe is impersonal or unconscious, personal consciousness in

**finite**spirits comes to wear the appearance of a blunder.At the same time Aristotle precludes the idea of a natural development of the mental series by the supposition that man contains, over and above a natural

**finite**soul inseparable from the body, a substantial and eternal principle (voi) which enters into the individual from without.Since a

**finite**number of particles is only susceptible of**finite**transpositions, it must happen (he says), in an eternal duration that every possible order or position will be tried an infinite number of times, and hence this world is to be regarded (as the Stoics maintained) as an exact reproduction of previous worlds.The thinker who sees man confronted by the infinite non-moral forces presumed by natural pantheism inevitably predominating over the

**finite**powers of men may appear to the modern Christian theologian or to the evolutionist as a hopeless pessimist, and yet may himself have concluded that, though the future holds out no prospect save that of annihilation, man may yet by prudence and care enjoy a considerable measure of happiness.As creation involves intention, desire, thought and work, and as these are properties which imply limit and belong to a

**finite**being, and moreover as the imperfect and circumscribed nature of this creation precludes the idea of its being the direct work of the infinite and perfect, the En Soph had to become creative, through the medium of ten Sephiroth or intelligences, which emanated from him like rays proceeding from a luminary.With these definitions it is now possible to prove the following six premisses applying to

**finite**cardinal numbers, from which Peano 2 has shown that all arithmetic can be deduced i.Owing to the correspondence between the

**finite**cardinals and the**finite**ordinals, the propositions of cardinal arithmetic and ordinal arithmetic correspond point by point.Under the general heading "Fundamental Notions" occur the subheadings "Foundations of Arithmetic," with the topics rational, irrational and transcendental numbers, and aggregates; "Universal Algebra," with the topics complex numbers, quaternions, ausdehnungslehre, vector analysis, matrices, and algebra of logic; and "Theory of Groups," with the topics

**finite**and continuous groups.If, however, as in practice, the light be heterogeneous, the source of

**finite**area, the obstacles in motion, and the discrimination of different directions imperfect, we are concerned merely with the mean brightness found by varying the arbitrary phase-relations, and this is obtained by simply multiplying the brightness due to a single aperture by the number of apertures (n) (see Interference Of Light, § 4).Hence, in accordance with the rule for compounding vector quantities, the resultant vibration at B, due to any

**finite**part of the primary wave, is represented in amplitude and phase by the chord joining the extremities of the corresponding arc (U2-0.1).Emphasis was made to fall on the reason, the conscience and the will of the

**finite**personality; and just as these were found to be native in him they were held to be immanent in the cause of his universe.The Poisson equation cannot, however, be applied in the above form to a region which is partly within and partly without an electrified conductor, because then the electric force undergoes a sudden change in value from zero to a

**finite**value, in passing outwards through the bounding surface of the conductor.Formulae of the calculus of

**finite**differences enable us from the chronograph records to infer the velocity and retardation of the shot, and thence the resistance of the air.As a single soul (world-soul) it belongs in essence and destination to the intelligible world; but it also embraces innumerable individual souls; and these can either submit to be ruled by the nous, or turn aside to the sensual and lose themselves in the

**finite**.Not only so, but in his review of Cousin (" Philosophy of the Unconditioned," in Discussions, pp. 12-15), he made conception the test of knowledge, argued that " the mind can conceive, and consequently can know, only the limited, and the conditionally limited," that " to think is to condition," that all we know either of mind or matter is " the phenomenal," that " we can never in our highest generalizations rise above the

**finite**," and concluded that we cannot conceive or know the unconditioned, yet must believe in its existence.The infinite or non-

**finite**is not necessarily known, ere the**finite**is negated, or in order to negate it; all that needs be known is the**finite**itself; and the contradictory negation of it implies no positive.This is important as a preliminary stage, but philosophy properly begins when it attempts to coordinate or systematize those convictions in harmony, to conciliate apparent contradiction and opposition, as between the correlative notions of

**finite**and infinite, the apparently conflicting notions of personality and infinitude, self and not-self; in a word, to reconcile the various sides of consciousness with each other.For example, model checkers offer very powerful reasoning abilities over

**finite**state systems.Two methods are compared which allow a simple, self-consistent solution based on

**finite**element analysis.The claim is that the allocation itself of observable algebras to

**finite**space-time regions suffices to account for the physical meaning of observables.Polycyclic Groups

**Finite**soluble groups and infinite polycyclic groups have special generating systems chosen in accordance with a subnormal series with cyclic factors.A few years ago, Colin Stirling and David Walker produced a tableau system for model-checking the linear time mu-calculus on

**finite**systems.In this paper, a case study is conducted on three classic topology optimization problems using different

**finite**element meshes.When the imaginary transfinite mathematics of the actual infinite is translated into real

**finite**terms, the results are nonsensical.Finally, we extend the theory of needed reduction from the

**finite**to the transfinite case.This allows routine computation of undamped vibration of any linear structure, for example by

**Finite**Element methods.We assume that the variance of the resource distribution is

**finite**.A

**finite**sample correction to the GMM variance estimate has been derived.Such tentative evidence is not yet sufficiently weighty to change the author 's convictions that the universe must be

**finite**in all respects.Do y'all know what a

**Finite**State Machine is?This

**finite**nature, coupled with the lack of personalization, makes some businesses a little wary of getting left holding the bag if some slick person manages to rack up more than he should and then simply ditches the card.Currently, no ideal replacement exists for the rapidly diminishing supply of fossil fuels, which are a

**finite**resource.In terms of industry growth, technology to harness renewable energy resources is gaining ground as the knowledge of earth's

**finite**fuel resources grows.It uses a renewable source of energy unlike the

**finite**resources of coal, natural gas, and petroleum products.Furnishings will fit into the room in a

**finite**number of configurations, but not all of them are pleasing or practical.Among the specific courses offered are options in botany,

**finite**math, calculus, astronomy, geology, classics, and political science.The thing about learning Christmas songs is that you have a

**finite**window when you can play them.You might consider allowing a teenager to take control of her own clothing budget; nothing makes a young woman a good shopper like awareness of how much things cost and the

**finite**size of her pocketbook.Save the

**finite**details for the presentation.Prepare yourself with the realization that although a kit will help you maximize your closet space, the space itself is still

**finite**.God, he says, is to be regarded not as an absolute but as an Infinite Person, whose nature it is that he should realize himself in

**finite**persons.In his conception of

**finite**personality he recurs to something like the monadism of Leibnitz.He admits two sources of knowledge - sensation and refiexion; and God is to him the Great First Cause, especially of our own existence (or of the existence of

**finite**minds).The world consists of a

**finite**number of atoms, which have in their own nature a self-moving force or principle.Later on he develops the materialistic view of Epicurus, only modifying it so far as to conceive of matter as

**finite**.The more celebrated and central thesis of the book - this

**finite**universe, the best of all such that are possible - also restates positions of Augustine and Aquinas.His argument for the Being of God is based on the hypothesis that thought - not individual but universal - is the reality of all things, the existence of this Infinite Thought being demonstrated by the limitations of

**finite**thought.This Essence is God, and includes within itself the

**finite**unities of man, reason and nature.In this all-important doctrine of the Sephiroth, the Kabbalah insists upon the fact that these potencies are not creations of the En Soph, which would be a diminution of strength; that they form among themselves and with the En Soph a strict unity, and simply represent different aspects of the same being, just as the different rays which proceed from the light, and which appear different things to the eye, are only different manifestations of one and the same light; that for this reason they all alike partake of the perfections of the En Soph; and that as emanations from the Infinite, the Sephiroth are infinite and perfect like the En Soph, and yet constitute the first

**finite**things.But the definition of the cardinal number of a class applies when the class is not

**finite**, and it can be proved that there are different infinite cardinal numbers, and that there is a least infinite cardinal, now usually denoted by o where to is the Hebrew letter aleph.If m and n are

**finite**cardinal numbers, the rational number m/n is the relation which any**finite**cardinal number x bears to any**finite**cardinal number y when n X x = m X y.Under the general heading "Analysis" occur the subheadings "Foundations of Analysis," with the topics theory of functions of real variables, series and other infinite processes, principles and elements of the differential and of the integral calculus, definite integrals, and calculus of variations; "Theory of Functions of Complex Variables," with the topics functions of one variable and of several variables; "Algebraic Functions and their Integrals," with the topics algebraic functions of one and of several variables, elliptic functions and single theta functions, Abelian integrals; "Other Special Functions," with the topics Euler's, Legendre's, Bessel's and automorphic functions; "Differential Equations," with the topics existence theorems, methods of solution, general theory; "Differential Forms and Differential Invariants," with the topics differential forms, including Pfaffians, transformation of differential forms, including tangential (or contact) transformations, differential invariants; "Analytical Methods connected with Physical Subjects," with the topics harmonic analysis, Fourier's series, the differential equations of applied mathematics, Dirichlet's problem; "Difference Equations and Functional Equations," with the topics recurring series, solution of equations of

**finite**differences and functional equations.Lastly Baxter attempted to prove that matter is

**finite**.Any space at every point of which there is a

**finite**magnetic force is called a field of magnetic force, or a magnetic field.If these equations could be assumed to hold when H is indefinitely small, it would follow that has a

**finite**initial value, from which there would be no appreciable deviation in fields so weak that bH was negligibly small in comparison with a.All forms of monism from Plotinus downwards tend to ignore personal individuality and volition, and merge all

**finite**existence in the featureless unity of the Absolute; this, indeed, is what inspires the passion of the protest against monism.Proceeding in this way, we may be able to express P= Q as the sum of a

**finite**number of terms k+m/r+n/r 2 +..The approach to the limit will therefore be by a series of jumps, each of which, however small, will be

**finite**; i.e.We cannot, for instance, say that the fraction C _2 I is arithmetically equal to x+I when x= I, as well as for other values of x; but we can say that the limit of the ratio of x 2 - I to x - I when x becomes indefinitely nearly equal to I is the same as the limit of x+ On the other hand, if f(y) has a definite and

**finite**value for y = x, it must not be supposed that this is necessarily the same as the limit which f (y) approaches when y approaches the value x, though this is the case with the functions with which we are usually concerned.If, on the other hand, the point be well immersed in the geometrical shadow, the earlier zones are altogether missing, and, instead of a series of terms beginning with

**finite**numerical magnitude and gradually diminishing to zero, we have now to deal with one of which the terms diminish to zero at both ends.According to Aristotle, "the first of Eleatic unitarians was not careful to say whether the unity which he postulated was

**finite**or infinite, but, contemplating the whole firmament, declared that the One is God."The method of electrical images will enable the stream function, )' to be inferred from a distribution of doublets,

**finite**in number when the surface is composed of two spheres intersecting at an angle 7r/m, where m is an integer (R.Taylor's Methodus Incrementorum Directa et Inversa (London, 1715) added a new branch to the higher mathematics, now designated the " calculus of

**finite**differences."In 1734 he also published Prodromus philosophiae ratiocinantis de infinito et causa finali creationis, which treats of the relation of the

**finite**to the infinite, and of the soul to the body, seeking to establish a nexus in each case as a means of overcoming the difficulty of their relation.In God there are three infinite and uncreated "degrees" of being, and in man and all things corresponding three degrees,

**finite**and created.It defines the condition which must be fulfilled by the potential at any and every point in an electric field, through which p is

**finite**and the electric force continuous.Combining this with the first law, for a Carnot cycle of

**finite**range, if H is the heat taken in at 0', and H" is the heat rejected at 0", the work W done in the cycle is equal to the difference H' - H", and we have the simple relations, W/(0' - o") =H'/o' =H" o".It is not necessary in this example that AB, CD should be adiabatics, because the change of volume BC is

**finite**.For a

**finite**change it is necessary to represent the path by a series of small steps, which is the graphic equivalent of integration along the path represented by the given relation between v and 0, or p and 0.Since the change of energy is independent of the path, the

**finite**change between any two given states may be found by integration along any convenient path.From the hypothesis of an external world a series of contradictions are deduced, such as that the world is both

**finite**and infinite, is movable and immovable, &c.; and finally, Aristotle and various other philosophers are quoted, to show that the external matter they dealt with, as mere potentiality, is just nothing at all.In it the union between the

**finite**self-consciousness and the infinite ego or God is handled in an almost mystical manner.Meanwhile, the same considerations had not been applied to time, so that in the days of Zeno of Elea time was still regarded as made up of a

**finite**number of ` moments,' while space was confessed to be divisible without limit.The universal or infinite is one that realizes itself in

**finite**particular minds and wills, not as accidents or imperfections of it, but as its essential form.It involves, it will be said, the reality of time, the dependence of the Infinite in the

**finite**, and therewith a departure from the whole line of Hegelian thought.It is to be remedied not by giving up the idea of the Infinite but by ceasing to think of the Infinite as of a being endowed with a static perfection which the

**finite**will merely reproduces, and definitely recognizing the forward effort of the**finite**as an essential element in Its self-expression.The general method of constructing formulae of this kind involves the use of the integral calculus and of the calculus of

**finite**differences.In the case of statistical data there is the further difficulty that there is no real continuity, since we are concerned with a

**finite**number of individuals.For the methods involving

**finite**differences, see references under DIFFERENCES, CALCULUS OF; and INTERPOLATION.The receiving apparatus had what we may term a personal equation, for the break of contact could only take place when the membrane travelled some

**finite**distance, exceedingly small no doubt, from the contact-piece.Since the curve represents a longitudinal disturbance in air it is always continuous, at a

**finite**distance from the axis, and with only one ordinate for each abscissa.If we rest on the synthesis here described, the energy of the matter, even the thermal part, appears largely as potential energy of strain in the aether which interacts with the kinetic energy associated with disturbances involving

**finite**velocity of matter.With reference to all such further refinements of theory, it is to be borne in mind that the perfect fluid of hydrodynamic analysis is not a merely passive inert plenum; it is also a continuum with the property that no

**finite**internal slip or discontinuity of motion can ever arise in it through any kind of disturbance; and this property must be postulated, as it cannot be explained.Now the kinetics of a medium in which the parts can have

**finite**relative motions will lead to equations which are not linear - as, for example, those of hydrodynamics - and the phenomena will be far more complexly involved.The primeval Being is, as opposed to the many, the One; as opposed to the

**finite**, the Infinite, the unlimited.On the principle that everything which is determined (

**finite**) is "negated" ("determinatio est negatio"), God, the ultimate reality must be entirely undetermined.Even philosophy with Hegel at this epoch was subordinate to religion; for philosophy must never abandon the

**finite**in the search for the infinite.The state is the consummation of man as

**finite**; it is the necessary starting-point whence the spirit rises to an absolute existence in the spheres of art, religion and philosophy.In the

**finite**world or temporal state, religion, as the**finite**organization of a church, is, like other societies, subordinate to the state.For the Son of God, in the immediate aspect, is the

**finite**world of nature and man, which far from being at one with its Father is originally in an attitude of estrangement.The earlier Hegelians had interpreted it in the sense that the world in its ultimate essence was not only spiritual but self-conscious intelligence whose nature was reflected inadequately but truly in the

**finite**mind.Metaphysically, all realities are parts of one ultimate reality; but logically, even philosophers think more often only of

**finite**realities, existing men, dogs, horses, &c.; and children know that their parents exist long before they apprehend ultimate reality.By it we perceive how God, the infinite, the absolute, the eternal, is yet not separated from the

**finite**, the temporal, the relative, but, through the incarnation, enters into humanity.The stresses in the bars would then be comparatively very great, although

**finite**.The main reason people are concerned with sustainable development is because of the fact that the world is a place of

**finite**materials.The well-known Treatise on Differential Equations appeared in 1859, and was followed, the next year, by a Treatise on the Calculus of

**Finite**Differences, designed to serve as a sequel to the former work.He may be said to furnish a further contribution to a metaphysical conception of evolution in his view of all

**finite**individual things as the infinite variety to which the unlimited productive power of the universal substance gives birth.And so on for all the

**finite**cardinals, which are thus defined successively.The definitions of the

**finite**ordinals can be expressed without use of the corresponding cardinals, so there is no essential priority of cardinals to ordinals.Similarly, a class of serial relations, called well-ordered serial relations, can be defined, such that their corresponding relation-numbers include the ordinary

**finite**ordinals, but also include relation-numbers which have many properties like those of the**finite**ordinals, though the fields of the relations belonging to them are not**finite**.P. Gordan first proved that for any system of forms there exists a

**finite**number of covariants, in terms of which all others are expressible as rational and integral functions.Thus it is used to translate the Platonic 'SEa, Et50s, the permanent reality which makes a thing what it is, in contrast with the particulars which are

**finite**and subject to change.For instance, there are the symbols A, D, E used in the calculus of

**finite**differences; Aronhold's symbolical method in the calculus of invariants; and the like.We have already seen that the Sephiric decade or the archetypal man, like Christ, is considered to be of a double nature, both infinite and

**finite**, perfect and imperfect.He holds that freedom is the inalienable prerogative of the

**finite**spirit; and this is the second point that distinguishes his theology from the heretical Gnosticism.Now if n be any

**finite**cardinal number, it can be proved that the class of those serial relations, which have a field whose cardinal number is n, is a relation-number.Given perfect information, frictionless markets, and other theoretical impossibilities, a

**finite**amount of utility can be achieved in that way.Is it

**finite**, or is it for all practical purposes infinite?This idea that there are a

**finite**number of jobs misses the point entirely of what makes a job.This

**finite**number of forms is said to constitute the complete system.