Infinity seen by physical and by matematical

8/8/2019 Infinity seen by physical and by matematical

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Summary:[1] Mathematics is a science, therefore it tell the truth, so what it says exist in world.[2] Plancks measure units of natural and Universal.[3] Point on the right called "the infinity point".[4] Semi-right from a beam called a semi-right infinite.

Rezumat:[1] Matematica este o tiin, prin urnare ea spune adevrul, deci ceea ce ea spune exist n lum[2] Unitile de msur naturale i Universale ale lui Planck.[3] Punctul de pe dreapt numit punctul infinit.[4] Semidreapta din un fascicul numitsemidreapta infinit.

An imperfect translation into English

Infinity seen by physical and by mathematical[1] Mathematics is a science, therefore it tell the truth, so what it says existWe must specify in advance what is mathematics. All admit that the world is a lot non-va

elements. Elements of the world are named entities. Some entities contain particles matter. These material entities. The subset of material entities is named the material world (it feel, is visible, can b

Figure 1 = Simplified structure of entities in the world

But there in the world and entities that do not contain particles matter. These are called ideationFor example: We recorded on a USB memory stick a book of geometry. It contains many ideas thread. For example: It contains the idea called "Tales's Theorem.". We weighed with maximum prequantity of matter from this USB stick. We will find grams X. Now we wipe physically the USB


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stick. This means to write only blanks in it. All ideas that existed were destroyed in the USB stickre-weigh the USB memory stick. Obviously we will find X grams also. We conclude: There are entities (Eg. Tales's theorem), but that they do not feel for the scales (They not attracted to the plhave not mass, they have not particles matter, they are without matter). Subset of ideational entitiin the world is called the world of ideas or the spiritual world.

Some ideational entities reflects material entities. They are called concrete ideas. Eg. All mothis glass of water have two atoms of hydrogen and one oxygen. This is a concrete idea that property of the material entity named "water." There are some ideas that reflect the propertieideational entities. They are abstract ideas. Subset of ideas that reflect the world entities (conabstracts) is called science.

If in the world exist a property of an entity that claims to reflect a scientific idea, then this is a trthe property does not exist, then the idea is false and non-scientific. Mathematics is the science thvery abstract and very general properties of existing entities in the wider world, but true ideas because and mathematics is also science.

We shall prove that the idea that infinite entities exist is false.Physics sees that everything is finite and in large and in small. The physics of microcosm find

small parts of space are not infinitely small. They are finite quanta. Astronomy notes that the Ufinite. Therefore, they found that the mathematical idea of infinity large and small is false. Thentities are non-existent into world.

[2] Plancks measure units of natural and UniversalIn 1906 Max Planck concluded that the world is complete quantified. So that nothing has cont

nothing is infinitely of little or infinitely of big.We know that there are three fundamental quantities: Mass, Length, Time (MLT). From these

measure for fundamental quantities we will deduce all other units (called "derived units"). We dderived units of measure so: We will calculate them from the mathematical relationships fundamental and derived quantities. These relations have long been established physics.

In conclusion: If we can establish that the mass, length and time are quantified (and therefore,not continue, as seems to macroscopic level), then the whole material world is quantified. The woris already quantified by the simple ideas. A simple idea is an idea that "is not composed" of other ithe logical operators. Simple ideas are expressed with simple sentences. A simple sentence ha predicate. Also and the truth value for ideas is quantified bivalent. An idea may be only or true or quantification of the ideas is used with successfully in computer science. The science by computeonly binary bits (or true or false, or T or F, or 1 or 0).

Planck start from a algebraic system with five equations (in generally accepted as true) unknowns. See Figure , mark no. 1. These unknowns will wear index P for to be easilyof the unknowns from system. This fact will elucidate many the solve the system. These unknowns

[1] The unit of measure of length (LP) which is called the Plancks length.

[2] The unit of measure of mass (MP) or the Plancks mass.[3] The unit of measure of time (tT) which is called the Planck's time.[4] The unit of measure of energy (EP) or the energy of Planck.[5] The unit of measure of force (FP) or force Planck.Those five equations of the system are given in the order (see figure). They are:[1] The space (in uniform motion) = speed time. If we harmonize at our objects, then we have

Planck length = photon speed in vacuum (maximum speed of relativity) unit of Planck time, LP = c tP.This is the first equation of the system.


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[2] Gravitational force of attraction = gravitational constant mass of an object mass of object / distance between them to squared. If we use this Newton's formula to our case, then we haunit of force = gravitational constant Planck's mass to squared / unit of Planck length to squaredP = G mP2 / LP2. This is the second equation of the system.

[3] We seek the definition the action in analytical mechanics for understand the term "action" a

is measured in energy units (Joules) x time (seconds). We have noted with = h / (2) Planck'reduced. This constant h is a quantum of action. Action has been defined by Laplace. He is the fanalytical mechanics. Laplace meant the action with S. The action of an object from the time t1 to

( )dt t U t V S t

t =2

1

)()(

Here V(t) is the kinetic energy of the object and U(t) of potential energy of the object. Since V energies and dt is time, then action is measured in J s. We infer: For to calculate the energy ca(the quantum of action of Planck), then h must to be divided with the time of action, so E = / t.apply to the case of our problem, then EP = / tP. Then this is the third equation of the system.

[4] By definition: Energy is mecanical work did by a force F (or which could to make it) and adirection of the force coincides with direction of travel on the distance L, so: E = mecanical work =our problem: The force is Planck's force FP and distance is the Planck length LP, then EP = FP LP. This is thefourth equation of the system.

[5] This last equation of the system is the famous the formula's Eistein (E = m c2). We will apply at thPlancks energy (EP). This energy is content in Planck's mass (mP). Here it is evident that the "c" is photspeed in a vacuum.

Figure 2 = Deduction the sizes for the units of natural measure (and universal)

By successive substitutions adequate selected (as shown in Figure ) we will system. We want to separate universal constants from unknowns (easily recognizable by the index


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In the form of system of final (with mark no. 15), unknowns are determined only by the constants: By the speed of photons in a vacuum (c), by universal constant for gravitation (G) and breduced of action Planck ().

Now we have those three natural units (mP, LP, tP) for the fundamental quantities of mass, length, (MLT). Their value (in International System of measures units) was calculated at Figure


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But with what (point) corresponds the origin (+O, infinitely small)? The origin (+ O) correspond point +I. This point is the large infinitely. This the explanation ask passage it at limit:

I x

x F y x x

+=+===++

1)( limlim

00 , so, for point +O correspond the point +I. For that matter, and vversa:

01

)( limlim +===++ x

x F y x x , so, for point +I corespond the point +O.

But there is a difference between +O and +I, namely: We can see the point +O (it is named thinfinitely), but we can not see the point +I (it is called the potential infinity). But this is only illusion, because we are very tiny compared to the infinitely large. We can not see than locally, a(point O). We have a perspective (an horizon) of a frog shortsighted. To see and the infinitely larghave a perspective (an horizon) of eagle. For this we will divide unevenly semi-axis (the univariable ) and they are not equal as we do locally (here, on our the planet, in around us). See the lan

In order not to complicate the understanding of the background we will not go into details of thdivisions. We will choose an appropriate function which (for a Cartesian coordinate for axles) withe length of the segment that will take. Function chosen is a transformation by translational composymmetry to the axis of function of echilatere hyperbola. Now, we will see and the infinite la because the points are crowded in around him +O and +I. With as points are the farther, with so tfunction has brought them closer towards point +I. We observe that (+ O + I) is an open segment, b points +A and +I were obtained by passing to the limit.

Now we remember and of the queue left behind: So we come back to negative semi-axle o(landmark 6). Now it is simple: Also, all points of negative semi-axle are equipotent with those osemi-axle. This we infer from the symmetry given by the function y = F(x) = x. We believe that is clear. This in order that we do not write much.

But now two large infinite appear: One is +I = + . It is large infinitely from positive semi-axle. Anois I = . It is large infinitely from negative semi-axle. But we will infer that they are identicorrespondent by inversion for point +I is point +O. The correspondent by inversion for point I isBut how +O = O, then +I = I.

We should see that infinitely large is unapproachable. Infinitely small is likewise unapproachabknowledge are imposible for human, because they do not exist. Astronomy sees that nothing exist athan 13.73 billion years light.

We are puting the question: If two semi-right (+ O; +I) and (O; I) have two common points,coincide. But we know well from the geometric intuition that these semi-right opposite (+ O; +I) an"not" coincide. The reason is that in eagle perspective what we call right-line is actually a clo(ellipse, circle etc.). We refer at the landmark 7 from "Figure " and the landmark 5 fro".

Also, any point on the right could be chosen as the origin or could be diametrically oppositorigin. Moreover: If we choose another point as the origin (P) on the right, then its opposite wouinfinitely large, while the former infinitely large will become a trivial point on right. Thus, we deduinfinite (large or small) is referentially dependent. In other words: These infinites were created breal (those which give the coordinates for those points). But real numbers are created by passing toat small-infinite of strings of rational-numbers. But this is a vicious circle. So, the infinites are int physics by a mistake of mathematics. So, they are not objective.

In conclusion: The mathematics consider that large and small infinites there are. This mistakefrom the Middle Ages, because they knew not physics for micro-cosmos and modern astronomy


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Planck showed that they do not exist, because everything is finite. We must to believe physics, b physics is using the theoretical deduction as mathematics, but also, experimental verification,observations and practical applications.

Planck showed previously that the only reality (natural and objective)is that on the right is a fin points.

We admite (astronomers concluded) that the Universe would be a giant sphere with a radius billion years-light. This radius has 13,73 billion years-light = 13,73 billion years-light 310+8 m / s(speed of light) 365 days / year 24 hours / day 3600 s / hour = 1,298967840 10+26 m 1,3 10+26 m.Diameter of the Universe / LP = 2 1,3 10+26 m / 1,6160 10-35 m = 2 8 1060 = 1,6 1061. So, the lots onatural numbers = maximum lots of points of the right-line. So, they are finished. If we will chooson the right and a positive meaning, then it is also the lots of integers numbers finite = ( 8 1060). Theseare natural cartesian coordinates for points on the right.

This number 2 8 1060 LP = 2 13,73 bilions yars-light = 2 1,3 10+26 m is true infinitely larg physical. The number 1 LP = 1,6160 10-35 m is (true) small infinitely physical. So mathematics has cre beautiful story of science fiction.

We can now easily generalize this infinites at the physical plane, at the entire three-dimensio

and at all existing physical quantities.For example: We will demonstrate for the second degree one-dimensional spaces. Hyperbgeometric-parables do not exist because they have ramifications at infinity. They are an illusionlocal perspective. We shall prove that exist only ellipses. See Figure .

Figure 3 = An ellipse seen out of the human horizont give or perception of ellipse or hyperbola or parabola

We consider a spherical surface passing through the planet and through a point on the edgUniverse (therefore, at a distance of 8 1060 LP = 13,73 LY = 1,3 10+26 m). We will delimit a sphericcalotte with the pole on the planet. Calotte is the human horizon for direct eyesight (less that 500 kthe plane).

[1] Inside this calotte we will draw an ellipse. It exists, because we see it in full.


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[2] Now we will draw an ellipse with only the tops into the limit human horizon. Now, we wilthe visual an hyperbole. See case A on the figure.

[3] If we will draw an ellipse only with a peak inside the calotte, but the second peak outside ththen we will perceive a parable. See case B on the figure.

The same phenomenon is repeated for quadrics. Now, we will consider a spherical body. It has

near of its surface. Now, the human horizon of direct vision is a sphere with a radius of about 50shall prove that exist only one quadric (it is ellipsoid).[1] If we draw an ellipsoid inside the horizon, then he is fully visible and, therefore, it exists).[2] The hyperboloid with two sheets is an ellipsoid which it has only one pair of extremes (top

horizon. They are seen clearly on his the drawing.[3] The hyperboloid with one sheet is an ellipsoid which it has two pairs of peaks (four) within

horizon. We see these two pairs of tops as follows: We will intersect the hyperboloid with the plThe two pairs of peaks are the two pairs of peaks of the ellipse of intersection.

[4] Elliptic paraboloid is an ellipsoid that has only one peak within horizon.[5] Hyperbolic paraboloid is an ellipsoid with two tops inside the horizon, but they are not a paiThus, we can continue to eliminate this mistake and from mathematics as they have already

colleagues in physics.[4] Semi-right from a beam called a semi-right infinite

Something similar is happening and with all line-right from beam (eg: In Figure , lanthe beam D). We will choose a semi-straight. For example: We choose the [DO (landmark 3


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But we will study how the physics sees the same problem: We will use figure , lan Now semi-straight points [OUI are not infinite. They have cardinal number 8 1060. This was deduced frothe Planck length. From the correspondence established above (point of semi-righteoussemi-straigh beam) we conclude that and the beam has also 8 1060 semi-straight.

In conclusion: The phantom named "infinite mathematical" was expelled by physicists and o

beam. So physicists have eliminated (everywhere) the infinitely out of physical. But if mathematicthemselves) would eliminate their the infinite, then it would have been better, because this infemath. We see how this do wrong: topology, analysis, etc. Infinite corrupts absolutely throughou because this came logically incorrect in mathematics (without theorem of existence, withouttheorem for closing of the lots of real numbers to the division by zero).

If you have objections or doubts, then I am at your disposal at address:[email protected]
mailto:[email protected]:[email protected]


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Textul original n limba romn

Infinitul vzut de fizic i de matematic[1] Matematica este o tiin, deci spune adevrul, deci exist ceea ce ea spune

Noi trebuie s precizm n prealabil ce este matematica. Toi admitem c lumea este o mulime elemente. Elementele lumii sunt numite entiti. Unele entiti conin particule materiale. Acestea entiti materiale. Submulimea entitilor materiale se numete lumea material (sesizabil pipibil).

Figura 3 = Structura simplificat de entiti ale lumii

ns exist n lume i entiti care nu conin particule materiale. Acestea se numesc entiti ideaexemplu: Noi am nregistrat pe o memorie stick USB o carte de geometrie. Ea conine foarte mucare le putem citi. De exemplu: Ea conine ideia numit Teorema lui Tales. Noi cntrim cu precizie cantitatea de materie din acest stick USB. Noi vom gsi X grame. tergem acum fizic mem

stick. Aceasta nseamn s scriem numai spaii goale n ea. Toate ideile care existau n USB stidistruse. Noi recntrim memoria USB stick. Evident c noi vom gsi deasemenea X graconcluzionm: Exist entiti ideatice (ex. Teorema lui Tales), dar c ele nu trag la cntar (nu sunt planet, nu au mas, nu au particule materiale, sunt imateriale). Submulimea entitilor ideatice elume se numete lumea ideilor sau lumea spiritual.

Unele entiti ideatice reflect entiti materiale. Acestea se numesc idei concrete. Ex. Toate mdin acest pahar cu ap au doi atomi de hidrogen i unul de oxigen. Aceasta este o idee concret car propietate a entitii materiale numit ap. Exist i unele idei care reflect proprieti ale alt


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ideatice. Acestea sunt idei abstracte. Submulimea ideilor care reflect entitile lumii (concrete sause numete tiin.

Dac exist n lume o proprietate a unei entiti pe care o idee tiinific pretinde c o reflecaceasta este o idee adevrat. Dac proprietatea nu exist, atunci ideia este fals i non tiinific. Meste tiina care reflect proprietile cele mai abstracte i cele mai generale ale entitilor existent

dar idei adevrate (nu fase), deoarece i matematica este tot o tiin. Noi vom demonstra c ideia c exist entiti infinite este fals.Fizica vede c totul este finit att n mare ct i n mic. Fizica microcosmosului constat c cele

pri din spaiu nu sunt infinit de mici, ci sunt cuante finite. Astronomia constat c Universul este acetia au constat c ideia de infinit matematic mare i mic este fals. Entitile infinite sunt inexlume.

[2] Unitile de msur naturale i Universale ale lui Planck n 1906 Max Planck a dedus c lumea este complet cuantificat (deci c nimic nu are conti

nimic nu este infinit de mic sau infinit de mare). Noi tim c exist trei mrimi fundamentale: Mas, Lungime, Timp (MLT). De la aceste u

msur pentru mrimile fundamentale noi vom deduce toate celelalte uniti (numite uniti derideducem toate unitile de msur derivate astfel: Noi le vom calcula din relaiile matematicmrimile fundamentale i cele derivate). Aceste relaii au fost stabilite de mult timp de fizic.

n concluzie: Dac putem stabili c masa, lungimea i timpul sunt cuantificate (i deci nu suntcum pare la nivel macroscopic), atunci toat lumea material este cuantificat. Lumea ideilorcuantificat de ctre ideile simple. O idee simpl este o idee care nu este compus din alte ideoperatorii logici. Ideile simple sunt exprimate cu propoziii simple. O propoziie simpl are predicat. Deasemeni i valoarea de adevr a ideilor este cuantificat bivalent. O idee poate fi adevrat sau fals. Aceast cuantificare a ideilor este folosit cu succes n informatic. Infomaticnumai binar (sau adevrat sau fals, sau A sau F, sau 1 sau 0).

Planck a plecat de la un sistem algebric cu cinci ecuaii (n general acceptate ca adevrate) A

figura reperul 1. Aceste necunoscute vor purta indicele P pentru a fi uor de deocunoscutele din sistem. Aceast fapt va elucida mult rezolvarea sistemului. Aceste necunoscute sunt[1] Unitatea de msur a lungimii (LP) care este numit lungimea Planck.[2] Unitatea de msur a masei (mP) sau masa Planck.[3] Unitatea de msur a timpului (tP) care este numit timpul Planck.[4] Unitatea de msur a energiei (EP) sau energia Planck.[5] Unitatea de msur a forei (FP) sau fora Planck.Cele cinci ecuaii ale sistemului sunt date n ordine (a se vedea figura). Ele sunt:[1] Spaiul (n micarea uniform) = viteza timpul. Dac noi particularizm la obiectele noastr

avem: Unitatea de lungime Planck = viteza fotonilor n vid (viteza maxim din relativitate) cuantPlanck, LP = c tP. Aceasta este prima ecuaie a sistemului.

[2] Fora de atracie gravitaional = constanta gravitaiei masa unui obiect masa celuiladistana dintre ele la ptrat. Dac utilizm aceast formul a lui Newton la cazul nostru, atunUnitatea de for Planck = Constanta gravitaiei masa lui Planck la ptrat / unitatea de lungime ptrat, FP = G mP2 / LP2. Aceasta este a doua ecuaie a sistemului.

[3] Noi am notat cu = h / (2) constanta redus a lui Planck. Aceast constant este o aciune. Noi cutm definiia aciunii n mecanica analitic pentru a nelege termenul de aciunemsoar ea n uniti de energie (Jouli) timp (secunde). Aciunea a fost definit de ctre Lapla


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fondatorul mecanicii analitice. Laplace a nsemnat aciunea cu S. Aciunea unui obiect de la tim1 la t2este:

( )dt t U t V S t

t =2

1

)()(

Aici V(t) este energia cinetic a obiectului i U (t) energia potenial a obiectului. Deoarece V energii i dt este timp, atunci aciunea se msoar n J s. Noi deducem: Pentru a calcula energia trde h (cuanta de aciune a lui Planck), atunci h trebuie mprit cu timpul ct acioneaz, deci E = noi vom aplica la cazul problemei noastre, atunci EP = / tP. Atunci aceasta este a treia ecuaie a sistemul

[4] Prin definiie: Energia este lucrul mecanic efectuat de o for F (sau care ar putea s l fac)direcia forei coincide cu direcia deplasrii pe distana L, deci E = lucrul mecanic = F L. n noastr: Fora este fora lui Planck FP i distana este lungimea lui Planck LP, atunci EP = FP LP. Aceastaeste a patra ecuaie a sistemului.

[5] Aceast ultim ecuaie a sistemului este celebra formul a lui Eistein (E = m c2). Noi vom aplica lenergia lui Planck (EP). Aceast energie este coninut n masa lui Planck (mP). Aici este evident c c esviteza fotonilor n vid.

Figura 2 = Deducerea dimensiunilor unitilor de msur naturale i Universale

Prin substituii succesive adecvat selectate (aa cum se arat n figura ) noi rsistemul. Noi vrem s separm constantele universale de necunoscute (uor de recunoscut dup ind

n forma final a sistemului (cu reperul 15) necunoscutele sunt determinate numai de ctre cuniversale: De viteza fotonilor n vid (c), de constanta atraciei universale (G) i de cuanta redus() a lui Planck.

Acum noi avem cele trei uniti de msur naturale (mP, LP, tP) pentru mrimile fundamentale de malungime, timp (MLT). Valoarea lor n SI este calculat pe figura la reperul 20.


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Aceste uniti de msur naturale au o proprietatea caracteristic. Ele dau dimensiuni extrmaxim de mici sau maxim de mari). Lungimea Planck i timpul Planck au dimensiuni maximTemperatura Planck i energia Planck au dimensiuni maxim de mari. Masa este o excepie.

Din mP, LP, tP deducem toate celelalte uniti de msur naturale. Noi folosim formulele de depdintre ele. Ele sunt cunoscute, deoarece se folosesc i n SI.

Rezolvarea sistemului a mai dat (n plus) i unitatea de for (FP) i unitatea de energie (EP). Noiam dedun plus i unitatea de msur a lui Planck (QP) pentru sarcina electric (pe figur la reperele 18, 19 i 21)Temperatura Planck TP a fost dedus la reperele 16, 17 i 21. Ea exprim temperatura maxim p

(1,417 10+32 K), Aceasta este temperatura la cuanta-moment zero, la Big-bang. Temperatura posibil (cuanta de rece sau cuanta de frig) este inversa temperaturii Planck (7,057 10 33 1 / K). Aceastaeste unitatea de msur natural Planck pentru temperatur. Aceaste este temperatura de 1 unititemperatur mai rece nu poate exista, Dac totui ea ar apare n Univers, atunci lumea material din existen (Big-crash), deoarece materia este format din cuante-eveniment care presupun eximicri perpetue.

Planck a dedus c nu exist nici un obiect infinit de mic sau o proprietate infinit de mic aa cmatematica. Noi deducem c nu exist nici infinitul mare, deoarece infinitul mare este inversul

mic. Deci toate obiectele sunt finite ca mrime. Deci, nu exist nici numere infinite:Putem acum calcula care esre cel mai mare numr natural: Nmax = Raza Universului / LP = 13,73 miliardani-lumin / LP = (13,73 10+9 ani-lumin 3 10+8 m / s (viteza fotonilor) 365 zile / an 24 ore /3600 s / or) / LP = (1,298967840 10+26 m) / (1,6160 10-35 m) = 8 10+60.

Volumul unei cuante-punct (al unui punct fizic) este (LP)3 = (1,6160 10-35)3 = 4,22 10-105 m3.Acest sistem de uniti de msur naturale descoperit de Planck este Universal (nu numai Int

uman, ci i eventual comun cu inteligenele extraterestre). El este complet, coerent i ar puteacoeficienii parazii care fac deosebirea ntre formulele matematice i formulele fizice.

[3] Punctul de pe dreapt numit punctul infinitMatematica consider c pe oricare dreapt exist dou puncte privilegiate numite punctul de c

zero i punctul de coordonat . A se vedea figura .Punctul, dreapta, planul i spaiu sunt noiuni fundamentale ale geometriei. Noi admitem ccunoscute intuitiv. Reperul 1 din figur este o dreapt. Noi tim axiomatic c dreapta este o mulimde puncte. Prin urmare, noi putem alege unul din ele. Fie el O. Dar n acest moment (vom dimediat) dreapta nu mai este ceea ce a fost la reperul 1. Pe ia a aprut infinitul mic (reper 2). IOricare punct de pe dreapt este ceea ce matematica numete punct de acumulare. Aceasta nseaoricare vecintatea a lui O exist cel puin un alt punct al dreptei diferit de O. Noi vom alege o simetric a lui O cu raza de 10 15 m. Atunci nseamn c va exista un alt punct P care aparine drepteieste la o deprtare de O mai mic de 10 15 m (ex. La 10 16 m). Noi putem alege atunci o alt vecinsimetric cu raza de 10 16 m i noi vom obine alt punct (R) i mai apropiat de O. n fizic acensemna c putem diviza o particul atomic n altele mai mici la infinit. Acesta este infinitu

microcosmosul. Ei bine, dar fizic microcosmosului a observat c nu este posibil divizarea sa la la o anumit vecintate simetric a particulei noi ne vom putea s mergem mai aproape de particvom putea divide pe particul sau noi nu avem energia necesar pentru a o divide. Aici este o pcunoatere care este definitiv nchis pentru om. Ceea ce este dincolo de aceast infim distan ovor ti niciodat. Este posibil ca eu s nu v fi convins, dar vom vedea ulterior pe alt cale c aadevrat.

Mai alegem un punct U diferit de O, deoarece (nu este aa?) sunt infinit de multe puncte i decunde alege. Minunea este c acum dreapta (cu origine de la reperul 2) devine din nou altceva. P


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acum i al doilea infinit. Acest infinit este infinitul mare. Infinitul mare este perechea infinitului vedea reperul 3. Acum noi v vom arta cum este ascuns pe dreapt infinitul mare. El este notat cum: Noi putem decide astfel: Punctul O trebuie s aib coordonata 0 i punctul U trebuicoordonata +1 uniti, deoarece noi am ales cum noi am vrut noi. Urmrim reperul 4.

Figura 4 = Ce crede matematica c ar fi infinitul

Pentru ca s nu complicm desenul noi am luat din dreapta dat numai semidreapta pozitivdeterminat de ctre origine (+O) i de ctre punctul U. Noi vom vedea c (i) ct de multe (puntre origine (+O) i punctul U, la fel de multe puncte sunt ntre infinitul mare (+I) i punctul Unumite numesc mulimi echipotente. Pentru a face aceasta noi folosim funcia y = F(x) = 1 / x; Aceast funcie (F) face o transformare numit inversiune. Astfel un punct (P) cu coordonata x caintervalului (+OU] corespunde cu un unic punct (P) cu coordonata 1 / x care aparine intervalulDe exemplu: Pentru punctul (P) cu coordonata + 0,125 corepunde un punct (P) cu coordonata 1 / 0Aceast funcie este inversabil x = F 1(y) = 1 / y. Noi deducem s funcia este i bijectiv. Aceasta ns

c punctele care aparin intervalului (+OU] corespund unu la unu cu punctele care aparin intervaDeci noi am dedus c aceste mulimi de puncte sunt echipotente. Evident c punctul U se corespnsui. Dar cu ce (punct) corespunde originea (+O, infinitul mic)? Originea (+O) corespunde cu pAceste punct este infinitul mare. Pentru a explica aceasta este necesar trecerea la limit:

I x

x F y x x

+=+===++

1)( limlim

00 , deci pentru punctul +O corespunde punctul +I. De altfel, i vicversa:


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01

)( limlim +===++ x

x F y x x , deci, pentru punctul +I corespunde punctul +O.

Dar exist o deosebire ntre +O i +I i anume: Noi putem s vedem punctul +O (acestra einfinitul actual), dar noi nu puten vedea punctul +I (el este numit infinitul potenial). Dar aceasta esiluzie uman, deoarece noi suntem foarte mici n comparaie cu infinitul mare. Noi nu putem velocal, n jurul nostru (punctul O). Noi avem o perspectiv (un orizont) a unei broate mioape. Peni infinitul mare noi trebuie s avem o perspectiv (un orizontul) de vultur. Pentru aceasta vneuniform semiaxa (unitile vor fi variabile) i ele nu sunt egale cum noi facem local (aici, pnoastr, n jurul nostru). A se vedea reperul 5.

Pentru a nu complica nelegerea de fond noi nu vom intra n detaliile acestei gradri. Se alege potrivit care (pentru o coordonat cartezian pentru axe) ne indic lungimea de segment pe care Funcia aleas este o trasformare prin translaie compus cu o simetrie fa de ax a funciei hechilatere. Acum vedem i infinitul mare +I, deoarece punctele sunt aglomerate n jurul lui +O i punctele sunt mai deprtate, cu att funcia de gradare le-a adus mai aproape de punctul +I. Noi ob(+O; +I) este un segment deschis, deoarece punctele +O i +I au fost obinute prin treceri la limit.

Noi ne amintim acum i de codia lsat n urm: Aa c noi revenim deci la semiaxa negativ(reper 6). Acum este simplu: De asemenea, toate punctele semidreptei negative sunt echipotente semidreptei pozitive. Aceasta noi deducem din simetria dat de ctre funcia y = F(x) = x. Noi figura este clar. Aceasta pentru ca noi s nu scriem mult.

Dar acum doi infinii mari apar: Unul este +I = + . El este infinitul mare de pe semi-axa pozitCellalt este I = . El este infinitul mare de pe semi-axa negativ. Dar noi vom deduce c ei sunt Corespondentul prin inversiune a lui +I este +O. Corespondentul prin inversiune a lui I este O+O = O, atunci i +I = I.

Noi ar trebui s vedem i c infinitul mare este inabordabil precum este i infinitul micunoaterea uman. Astronomia vede c nimic nu exist la deprtare mai mare de 13,73 miliarde an

Noi punem acum ntrebarea: Dac dou semidrepte (+O; +I) i (O; I) au dou puncte comuele coincid. Dar noi tim bine din intuiia geometric c aceste semidrepte opuse (+O; U) i (O;coincid. Explicaia este c n perspectiva vulturului ceea ce noi numim linie dreapt este de fapnchis (elips, cerc etc.). Ne referim la reperul 7 din figura i la reperul 5 din figura


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S admitem concluzia astronomilor c Universul ar fi o gigantic sfer cu raza de 13,73 miliardlumin. Aceast raz are 13,73 miliarde ani lumin = 13,7310+9 ani-lumin 310+8 m / s (viteza lumini 365 zile / an 24 ore / zi 3600 s / or = 1,298967840 10+26 m 1,3 10+26 m.

Numrul natural maxim de puncte este: Diametrul Universului / LP = 2 1,3 10+26 m / 1,6160 10-35 m= 2 8 1060 = 1,6 1061. Deci, mulimea numerelor naturale = mulimea maxim de puncte a drepte

ele sunt finite. Dac noi vom alege o origine pe dreapt i un sens pozitiv, atunci mulimea numereeste deasemeni finit = 8 1060. Acestea sunt coordonatele carteziene ntregi ale punctelor de pe dre Numrul 2 8 1060 uniti Planck = 2 13,73 LY = 2 1,3 10+26 m este adevratul infinit mare fiz

Numrul 1 LP = 1,6160 10-35 m este adevratul infinit mic fizic. Deci matematica a creat o fru poveste tiinifico-fantastic.

Noi putem acum generaliza acum aceti infinii fizici la plane, la ntregul spaiu tridimensional mrimile fizice existente.

Ca exemplu: Noi vom demonstra pentru spaiile unidimensionale de gradul doi. Noi dedhiperbole i parabole nu exist, deoarece au ramuri la infinit. Ele sunt o iluzie dat de perspectiva lvom demonstra c exist numai elipse. A se vedea figura .

Figura 5 = O elips vzut din orizontul uman d sau percepie de elips sau de hiperbol sau de parabol

Noi considerm o suprafa sferic care trece prin planet i prin un punct de la marginea Univ(deci la o distan de 8 1060 LP = 13,73 LY = 1,3 10+26 m). Noi vom delimita o calot sferic cu polul p

planet. Calota este orizontul uman al vederii directe (cel mult 500 km, chiar din avion).[1] n interiorul acestei calote noi vom desena o elips. Ea exist pentru c noi o vedem n ntre[2] Acum noi vom desena o elips numai cu vrfurile n limita orizontului uman. Acum noi vo

vizual o hiperbol. A se vedea cazul A de pe figur.[3] Dac noi desenm o elips numai cu un vrf n interiorul calotei, dar cu al doilea vrf n afa

orizontului, atunci noi vom percepe o parabol. A se vedea cazul B de pe figur.


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Acelai fenomen se repet pentru cuadrice. Acum, noi considerm un corp sferic (plin) la care este aproape de suprafaa lui. Acum, orizontul vederii umane este o sfer cu raza de circa 1000 Kmdemonstra c exist numai o cuadric (anume elipsoidul).

[1] Dac noi vom desena un elipsoid n interiorul orizontului, atunci el este complet vizibil i dexist.

[2] Hiperboloidul cu dou pnze este un elipsoid care el are numai o pereche de vrfuri n orizonostru. Ele sunt vzute clar pe desenul lui.[3] Hiperboloidul cu o pnz este un elipsoid care are dou perechi (patru) de vrfuri n interio

orizontului uman. Noi vedem aceste dou perechi de vrfuri astfel: Intersectm hiperboloidul cu plCele dou perechi de vrfuri sunt cele dou perechi de vrfuri ale elipsei de intersecie.

[4] Paraboloidul eliptic este un elipsoid care are numai un vrf n interiorul orizontului.[5] Paraboloidul hiperbolic este un elipsoid care are dou vrfuri n interiorul orizontului, dar c

sunt ns o pereche.Astfel noi putem continua eliminarea acestei greeli i din matematic aa cum deja au fcut-o

notri din fizic.

[4] Semidreapta din un fascicul numit semidreapta infinitCeva similar se petrece i cu dreptele unui fascicul (ex: n figura


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lungimea lui Planck. Din corespondena stabilit anterior (punct al semidrepteisemidreapt afascicului) noi deducem c i fasciculul are tot 8 1060 semidrepte.

n concluzie: Fantoma numit infinit matematic a fost expulzat de ctre fizicieni i din fascifizicienii au eliminat de pretutindeni infinitul din fizic. Dar dac matematicienii (chiar ei nii) ainfinitul lor, atunci ar fi fost mai bine, deoarece acesta infecteaz toat matematica. Noi vedem c

face greit: topologia, analiza etc. Infinitul stric absolut toat tiina, deoarece a intrat clanmatematic (fr teorem de existen, fr teorem de existen a nchiderii mulimii numeremprirea prin zero).

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Infinity seen by physical and by matematical

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