Notations imposed by the Internet:
- We express exponents by the sign ^. Ex: 2^3 = 8
- We express lower indices by the word "index". Ex: Formula for water is: H(index 2)O
Infinity seen by physical and by mathematical
[1] Mathematics is a science, therefore it tell the truth, so what it says exist
- We must specify in advance what is mathematics. All admit that the world is a lot non-vacuum of elements. Elements of the world are named entities. Some entities contain particles matter. These are named material entities. The subset of material entities is named the material world (it feel, is visible, can be touch).
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 ideational entities. For example: We recorded on a USB memory stick a book of geometry. It contains many ideas that we can read. For example: It contains the idea called "Tales's Theorem.". We weighed with maximum precision the quantity of matter from this USB stick. We will find grams X. Now we wipe physically the USB memory stick. This means to write only blanks in it. All ideas that existed were destroyed in the USB stick. We will re-weigh the USB memory stick. Obviously we will find X grams also. We conclude: There are ideational entities (Eg. Tales's theorem), but that they do not feel for the scales (They not attracted to the planet, they have not mass, they have not particles matter, they are without matter). Subset of ideational entities existing in 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 molecules in this glass of water have two atoms of hydrogen and one oxygen. This is a concrete idea that reflects a property of the material entity named "water." There are some ideas that reflect the properties of other ideational entities. They are abstract ideas. Subset of ideas that reflect the world entities (concretes or abstracts) is called science.
- If in the world exist a property of an entity that claims to reflect a scientific idea, then this is a true idea. If the property does not exist, then the idea is false and non-scientific. Mathematics is the science that reflects very abstract and very general properties of existing entities in the wider world, but true ideas (not fase), 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 finds that the small parts of space are not infinitely small. They are finite quanta. Astronomy notes that the Universe is finite. Therefore, they found that the mathematical idea of infinity large and small is false. The infinite entities are non-existent into world.
[2] Planck’s measure units of natural and Universal
- In 1906 Max Planck concluded that the world is complete quantified. So that nothing has continuity and nothing is infinitely of little or infinitely of big.
- We know that there are three fundamental quantities: Mass, Length, Time (MLT). From these units of measure for fundamental quantities we will deduce all other units (called "derived units"). We deduce all derived units of measure so: We will calculate them from the mathematical relationships between 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, these are not continue, as seems to macroscopic level), then the whole material world is quantified. The world of ideas is already quantified by the simple ideas. A simple idea is an idea that "is not composed" of other ideas using the logical operators. Simple ideas are expressed with simple sentences. A simple sentence has a single predicate. Also and the truth value for ideas is quantified bivalent. An idea may be only or true or false. This quantification of the ideas is used with successfully in computer science. The science by computers is using only 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) and five unknowns. See Figure , mark no. 1. These unknowns will wear index P for to be easily distinctly of the unknowns from system. This fact will elucidate many the solve the system. These unknowns are:
- [1] The unit of measure of length L(index P) which is called the Planck’s length.
- [2] The unit of measure of mass M(index P) or the Planck’s mass.
- [3] The unit of measure of time t(index T) which is called the Planck's time.
- [4] The unit of measure of energy E(index P) or the energy of Planck.
- [5] The unit of measure of force F(index P) 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: Unit of Planck length = photon speed in vacuum (maximum speed of relativity) × unit of Planck time, L(index P) = c × t(index P). This is the first equation of the system.
- [2] Gravitational force of attraction = gravitational constant × mass of an object × mass of the other object / distance between them to squared. If we use this Newton's formula to our case, then we have: Planck unit of force = gravitational constant × Planck's mass to squared / unit of Planck length to squared, F(index P) = G × m(inex P)^2 / L(index P)^2. This is the second equation of the system.
- [3] We seek the definition the action in analytical mechanics for understand the term "action" and why it is measured in energy units (Joules) x time (seconds). We have noted with h = h / (2pi) Planck's constant reduced. This constant h is a quantum of action. Action has been defined by Laplace. He is the founder of analytical mechanics. Laplace meant the action with S. The action of an object from the time t1 to t2 is:
- Here V(t) is the kinetic energy of the object and U(t) of potential energy of the object. Since V and U are energies and dt is time, then action is measured in J × s. We infer: For to calculate the energy carried by h (the quantum of action of Planck), then h must to be divided with the time of action, so E = h / t. If we will apply to the case of our problem, then E(index P) = h / t(index P). 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 at wich the direction of the force coincides with direction of travel on the distance L, so: E = mecanical work = F × L. In our problem: The force is Planck's force F(index P) and distance is the Planck length L(index P), then E(index P) = F(index P) × L(index P). This is the fourth equation of the system.
- [5] This last equation of the system is the famous the formula's Eistein (E = m × c^2). We will apply at the Planck’s energy E(index P). This energy is content in Planck's mass m(index P). Here it is evident that the "c" is photons speed 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 solve the system. We want to separate universal constants from unknowns (easily recognizable by the index P).
- In the form of system of final (with mark no. 15), unknowns are determined only by the universal constants: By the speed of photons in a vacuum (c), by universal constant for gravitation (G) and by quantum reduced of action Planck (h).
- Now we have those three natural units {m(index P), L(index P), t(index P)} for the fundamental quantities of mass, length, time (MLT). Their value (in International System of measures units) was calculated at Figure , at the marker 20.
- These natural units have a feature property. They give extreme sizes (or maximum of small or maximum of big). Planck length and Planck time have sizes maximum of small. Max Planck temperature and Planck energy have size maximum of big. Mass is a exception.
- From the m(index P), L(index P), t(index P) we infer all the other natural units measure. We use the formulas of dependency between them. They are known, because they are used and in SI.
- Solving the system gave (in addition) and the unity of force F(index P) and unity of energy E(index P). We deducted in addition and Planck's measure unit Q(index P) for electric charge (on figure at landmarks 18, 19 and 21).
- Planck temperature was deduced at the marker no. 16, 17 and 21. It expresses the maximum possible temperature (1,417 × 10^+32 K). This is the temperature at zero quantum-moment, at the Big-bang. Lowest possible temperature (quantum of cold) is the inverse Planck temperature (7,057 × 10^–33 * 1 / K). This is the natural unit Planck for temperature. This is a temperature of 1 Planck units. A colder temperature it can not exist. However, if it would appear in the universe, then the material world would disappear from existence (Big-crash), because matter is made of quanta-event involving the existence of perpetual motion.
- Planck deduced that there is no infinitely small object or a property infinitely small, such maths say. We infer that there is no neither infinity large, because the infinity large is reverse for infinity small. So, all objects are finite in size. So, there is no infinite numbers:
- We can now calculate which is the largest natural number: Nmax = The Universe radius / L(index P) = 13,73 billion light-years / L(index P) = (13,73 × 10^+9 light-years × 3 × 10^+8 m / s (the speed of photons) × 365 days / year × 24 hours / day × 3600 s / h) / L(index P) = (1,298967840 × 10^+26 m) / (1,6160 × 10^-35 m) = 8 × 10^+60.
- The volume of a quantum-dot (a physical point) is (index LP)^3 = (1,6160 × 10^-35)^3 = 4,22 × 10^-105 m^3.
- This system of natural measure units discovered by Planck is the Universal (not only for global people, but possibly common with extraterrestrial intelligences). He is completely, is coherently and could abolish the coefficients parasites wich make the difference between physical fornulas and mathematical formulas.
[3] Point on the right called "the infinity point"
- Mathematics believes that there are two points with privileges on right. They are called the point of coordinate zero and point of coordinate infinite: ± infinity. See Figure .
- Point, right, plane and space are fundamental concepts of geometry. We admit that they are known intuitively. Mark 1 from figure is a straight line. We know axiomatically that the straight is an infinite lots of points. Therefore, we can choose one of them. Whether he ±O. But at the moment (we will demonstrate immediately) the line-straight is not same with what it was at the landmark 1. On it came the infinite small (landmark 2). Here's why: Any point on the right is what mathematics called accumulation point. This means that into any neighborhood of ±O exist at least one another point of straight-line (different of ±O). We will choose a symmetric neighborhood of O with radius of ±10^-15 m. It means that there will be another point P that belongs to the line-right and which is at a distance of ±O less than as 10^-15 m (Eg. at 10&-16 m). Then we can choose another symmetric neighborhood with a radius of 10^-16 m and we will obtain another point (R) and closer of ±O. In physics this would mean that we can divide a atomic particle into others smaller to infinity. This is the small infinity or microcosm. Well, but the physical of microcosm noted that it is not possible to be divide it at indefinitely. From a certain symmetrical proximity of the particle we will can not to go nearer of particle, we do not will can divide on particle or we do not have the necessary energy for to divide it. Here is a gateway towards knowledge that is definitively closed for humans. What is beyond this tiny distance, people will never know. It is possible that I do not will be persuaded you, but we will see later in another way that this is true.
- More we choose a point (U) different from ± O, because (not?) are infinitely many points and therefore we have of where a choice. The miracle is that now line-right (with origin from landmark 2) becomes something else again. On it came now and second infinite. This infinite is the large infinite. Large infinite is pair at small infinite. See the landmark 3. Now we will show you as it is hidden infinitely large on right. It is denoted by ± I. Here's how: We can decide thus: Point ± O must to have „0” coordinated and point U must to have „+1” coordinated, because we have chosen how we wanted. We follow the landmark 4.
Figura 3 = What thinks the math that would be infinity
- In order that we do not must complicate the design, we have taken out of given line-right only semi-right positive. It is determined by the origin (+O) and by the point U. We will see how much (points) are between origin (+O) and point U, also many points are between infinitely large (+I) and point U. They are called equipotenta lots of. To do this we use the function y = F (x) = 1 / x; (landmark 4). This function (F), make a transformation named inversion. Thus a point (P) with coordinate x that belongs to the interval (OU] corresponds to a single point (P') with coordinate 1 / x that belongs the interval [U, I). For example: For the point (P) with coordinated + 0,125 corepunde a point (P') with coordinated 1 / 0,125 = +8. This function is invertible x = F–1(y) = 1 / y. Therefore, we infer that the function is and bijective. This means that the points belonging to the interval (+ OU] corespond one at one with the points that belong to the interval [UI). So, we have inferred that these sets of points are equipotent. It is obvious that the point "U" corresponds to himself. But with what (point) corresponds the origin (+O, infinitely small)? The origin (+ O) corresponds with the point +I. This point is the large infinitely. This the explanation ask passage it at limit:
- so, for point +O correspond the point +I. For that matter, and vice versa:
- 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 the topical infinitely), but we can not see the point +I (it is called the potential infinity). But this is only a human illusion, because we are very tiny compared to the infinitely large. We can not see than locally, around our (point ±O). We have a perspective (an horizon) of a frog shortsighted. To see and the infinitely large we must have a perspective (an horizon) of eagle. For this we will divide unevenly semi-axis (the units will be variable ) and they are not equal as we do locally (here, on our the planet, in around us). See the landmark 5.
- In order not to complicate the understanding of the background we will not go into details of this unequal divisions. We will choose an appropriate function which (for a Cartesian coordinate for axles) will indicate the length of the segment that will take. Function chosen is a transformation by translational composed with a symmetry to the axis of function of echilatere hyperbola. Now, we will see and the infinite large (+I), because the points are crowded in around him +O and +I. With as points are the farther, with so the scaling function has brought them closer towards point +I. We observe that (+ O + I) is an open segment, because the 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 of on right (landmark 6). Now it is simple: Also, all points of negative semi-axle are equipotent with those of positive semi-axle. This we infer from the symmetry given by the function y = F(x) = –x. We believe that the Figure 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. Another is –I = –?. It is large infinitely from negative semi-axle. But we will infer that they are identical. The correspondent by inversion for point +I is point +O. The correspondent by inversion for point –I is point –O. But how +O = –O, then +I = –I.
- We should see that infinitely large is unapproachable. Infinitely small is likewise unapproachable. These knowledge are imposible for human, because they do not exist. Astronomy sees that nothing exist away more than 13.73 billion years light.
- We are puting the question: If two semi-right (+ O; +I) and (–O; –I) have two common points, then they coincide. But we know well from the geometric intuition that these semi-right opposite (+ O; +I) and (–O; –I) "not" coincide. The reason is that in eagle perspective what we call right-line is actually a closed curve (ellipse, circle etc.). We refer at the landmark 7 from "Figure " and the landmark 5 from "Figure ".
- Also, any point on the right could be chosen as the origin or could be diametrically opposite point of origin. Moreover: If we choose another point as the origin (P) on the right, then its opposite would become infinitely large, while the former infinitely large will become a trivial point on right. Thus, we deduce that the infinite (large or small) is referentially dependent. In other words: These infinites were created by numbers real (those which give the coordinates for those points). But real numbers are created by passing to boundary at small-infinite of strings of rational-numbers. But this is a vicious circle. So, the infinites are introduced in physics by a mistake of mathematics. So, they are not objective.
- In conclusion: The mathematics consider that large and small infinites there are. This mistake remained from the Middle Ages, because they knew not physics for micro-cosmos and modern astronomy. But now, Planck showed that they do not exist, because everything is finite. We must to believe physics, because the physics is using the theoretical deduction as mathematics, but also, experimental verification, scientific observations and practical applications.
- Planck showed previously that the only reality (natural and objective)is that on the right is a finite lots of points.
- We admite (astronomers concluded) that the Universe would be a giant sphere with a radius of 13.73 billion years-light. This radius has = 13,73 billion years-light = 13,73 billion years-light × 3×10^+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 / L(incex P) = 2 × 1,3 × 10^+26 m / 1,6160 × 10^-35 m = 2 × 8 × 10^60 = 1,6 × 10^61. So, the lots of natural numbers = maximum lots of points of the right-line. So, they are finished. If we will choose an origin on the right and a positive meaning, then it is also the lots of integers numbers finite = (? 8 × 10^60). These are natural cartesian coordinates for points on the right.
- This number 2 × 8 × 10^60 L(index P) = 2 × 13,73 bilions yars-light = 2 × 1,3 × 10^+26 m is true infinitely large physical. The number 1 L(incex P) = 1,6160 × 10^-35 m is (true) small infinitely physical. So mathematics has created a beautiful story of science fiction.
- We can now easily generalize this infinites at the physical plane, at the entire three-dimensional space and at all existing physical quantities.
- For example: We will demonstrate for the second degree one-dimensional spaces. Hyperboles and geometric-parables do not exist because they have ramifications at infinity. They are an illusion given the local perspective. We shall prove that exist only ellipses. See Figure .
Figure 4 = 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 edge of the Universe (therefore, at a distance of 8 × 10^60 L(index P) = 13,73 LY = 1,3 × 10^+26 m). We will delimit a spherical calotte with the pole on the planet. Calotte is the human horizon for direct eyesight (less that 500 km, even in the plane).
- [1] Inside this calotte we will draw an ellipse. It exists, because we see it in full.
- [2] Now we will draw an ellipse with only the tops into the limit human horizon. Now, we will perceive the 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 the horizon, then 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 the planet near of its surface. Now, the human horizon of direct vision is a sphere with a radius of about 500 Km. We shall 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 (tops) into our 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 the uman horizon. We see these two pairs of tops as follows: We will intersect the hyperboloid with the plane z = 0. The 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 pair.
- Thus, we can continue to eliminate this mistake and from mathematics as they have already done our 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 , landmark 2, the beam D). We will choose a semi-straight. For example: We choose the [DO (landmark 3, Figure . It has the polar coordinate = zero. Then, the infinitely small for all semi-right of beam will appear, because we can find some semi-right, who is infinite close to it. For this: See landmark 4 on figure. Here is represented and a right (OUIO) with her point at infinity. But (out of the eagle's horizon) we will see that the line-right is in fact a circle. Mathematics says that right (OUIO) has infinitely of many points. The center D (out of beam) and an arbitrary point M from right (OUIO, which we see to be a circle) determines semi-right "[DM" (out of beam). Now we fix our attention on semi-right [OUI. We have a bijective function defined on the lots of points semi-right, with values in lots of semi-right of beam.
Figura 5 = The beam centered on a given point has infinitely many straights
- Therefore, we have made a bijective correspondence between points on semi-right elected “[OUI” and all semi-right of the beam (D). So, any point on the semi-right [OUI corresponds to a semi-straight of beam (“one” to “one”). It follows that: Points O and I correspond with semi-right [DO (infinitely small for beam) and [DI (which is infinitely large for beam).
- But we will study how the physics sees the same problem: We will use figure , landmark 5. Now semi-straight points [OUI are not infinite. They have cardinal number 8 × 10^60. This was deduced from the Planck length. From the correspondence established above („point of semi-righteous” ?? „semi-straight beam”) we conclude that and the beam has also 8 × 10^60 semi-straight.
- In conclusion: The phantom named "infinite mathematical" was expelled by physicists and out of the beam. So physicists have eliminated (everywhere) the infinitely out of physical. But if mathematicians (even themselves) would eliminate their the infinite, then it would have been better, because this infects all the math. We see how this do wrong: topology, analysis, etc. Infinite corrupts absolutely throughout science, because this came logically incorrect in mathematics (without theorem of existence, without existence theorem 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:
- [1] The unit of measure of length L(index P) which is called the Planck’s length.
- [2] The unit of measure of mass M(index P) or the Planck’s mass.
- [3] The unit of measure of time t(index T) which is called the Planck's time.
- [4] The unit of measure of energy E(index P) or the energy of Planck.
- [5] The unit of measure of force F(index P) 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: Unit of Planck length = photon speed in vacuum (maximum speed of relativity) × unit of Planck time, L(index P) = c × t(index P). This is the first equation of the system.
- [2] Gravitational force of attraction = gravitational constant × mass of an object × mass of the other object / distance between them to squared. If we use this Newton's formula to our case, then we have: Planck unit of force = gravitational constant × Planck's mass to squared / unit of Planck length to squared, F(index P) = G × m(inex P)^2 / L(index P)^2. This is the second equation of the system.
- [3] We seek the definition the action in analytical mechanics for understand the term "action" and why it is measured in energy units (Joules) x time (seconds). We have noted with h = h / (2pi) Planck's constant reduced. This constant h is a quantum of action. Action has been defined by Laplace. He is the founder of analytical mechanics. Laplace meant the action with S. The action of an object from the time t1 to t2 is:
- Here V(t) is the kinetic energy of the object and U(t) of potential energy of the object. Since V and U are energies and dt is time, then action is measured in J × s. We infer: For to calculate the energy carried by h (the quantum of action of Planck), then h must to be divided with the time of action, so E = h / t. If we will apply to the case of our problem, then E(index P) = h / t(index P). 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 at wich the direction of the force coincides with direction of travel on the distance L, so: E = mecanical work = F × L. In our problem: The force is Planck's force F(index P) and distance is the Planck length L(index P), then E(index P) = F(index P) × L(index P). This is the fourth equation of the system.
- [5] This last equation of the system is the famous the formula's Eistein (E = m × c^2). We will apply at the Planck’s energy E(index P). This energy is content in Planck's mass m(index P). Here it is evident that the "c" is photons speed in a vacuum.
- By successive substitutions adequate selected (as shown in Figure
- In the form of system of final (with mark no. 15), unknowns are determined only by the universal constants: By the speed of photons in a vacuum (c), by universal constant for gravitation (G) and by quantum reduced of action Planck (h).
- Now we have those three natural units {m(index P), L(index P), t(index P)} for the fundamental quantities of mass, length, time (MLT). Their value (in International System of measures units) was calculated at Figure
- These natural units have a feature property. They give extreme sizes (or maximum of small or maximum of big). Planck length and Planck time have sizes maximum of small. Max Planck temperature and Planck energy have size maximum of big. Mass is a exception.
- From the m(index P), L(index P), t(index P) we infer all the other natural units measure. We use the formulas of dependency between them. They are known, because they are used and in SI.
- Solving the system gave (in addition) and the unity of force F(index P) and unity of energy E(index P). We deducted in addition and Planck's measure unit Q(index P) for electric charge (on figure at landmarks 18, 19 and 21).
- Planck temperature was deduced at the marker no. 16, 17 and 21. It expresses the maximum possible temperature (1,417 × 10^+32 K). This is the temperature at zero quantum-moment, at the Big-bang. Lowest possible temperature (quantum of cold) is the inverse Planck temperature (7,057 × 10^–33 * 1 / K). This is the natural unit Planck for temperature. This is a temperature of 1 Planck units. A colder temperature it can not exist. However, if it would appear in the universe, then the material world would disappear from existence (Big-crash), because matter is made of quanta-event involving the existence of perpetual motion.
- Planck deduced that there is no infinitely small object or a property infinitely small, such maths say. We infer that there is no neither infinity large, because the infinity large is reverse for infinity small. So, all objects are finite in size. So, there is no infinite numbers:
- We can now calculate which is the largest natural number: Nmax = The Universe radius / L(index P) = 13,73 billion light-years / L(index P) = (13,73 × 10^+9 light-years × 3 × 10^+8 m / s (the speed of photons) × 365 days / year × 24 hours / day × 3600 s / h) / L(index P) = (1,298967840 × 10^+26 m) / (1,6160 × 10^-35 m) = 8 × 10^+60.
- The volume of a quantum-dot (a physical point) is (index LP)^3 = (1,6160 × 10^-35)^3 = 4,22 × 10^-105 m^3.
- This system of natural measure units discovered by Planck is the Universal (not only for global people, but possibly common with extraterrestrial intelligences). He is completely, is coherently and could abolish the coefficients parasites wich make the difference between physical fornulas and mathematical formulas.
- Mathematics believes that there are two points with privileges on right. They are called the point of coordinate zero and point of coordinate infinite: ± infinity. See Figure
- Point, right, plane and space are fundamental concepts of geometry. We admit that they are known intuitively. Mark 1 from figure is a straight line. We know axiomatically that the straight is an infinite lots of points. Therefore, we can choose one of them. Whether he ±O. But at the moment (we will demonstrate immediately) the line-straight is not same with what it was at the landmark 1. On it came the infinite small (landmark 2). Here's why: Any point on the right is what mathematics called accumulation point. This means that into any neighborhood of ±O exist at least one another point of straight-line (different of ±O). We will choose a symmetric neighborhood of O with radius of ±10^-15 m. It means that there will be another point P that belongs to the line-right and which is at a distance of ±O less than as 10^-15 m (Eg. at 10&-16 m). Then we can choose another symmetric neighborhood with a radius of 10^-16 m and we will obtain another point (R) and closer of ±O. In physics this would mean that we can divide a atomic particle into others smaller to infinity. This is the small infinity or microcosm. Well, but the physical of microcosm noted that it is not possible to be divide it at indefinitely. From a certain symmetrical proximity of the particle we will can not to go nearer of particle, we do not will can divide on particle or we do not have the necessary energy for to divide it. Here is a gateway towards knowledge that is definitively closed for humans. What is beyond this tiny distance, people will never know. It is possible that I do not will be persuaded you, but we will see later in another way that this is true.
- More we choose a point (U) different from ± O, because (not?) are infinitely many points and therefore we have of where a choice. The miracle is that now line-right (with origin from landmark 2) becomes something else again. On it came now and second infinite. This infinite is the large infinite. Large infinite is pair at small infinite. See the landmark 3. Now we will show you as it is hidden infinitely large on right. It is denoted by ± I. Here's how: We can decide thus: Point ± O must to have „0” coordinated and point U must to have „+1” coordinated, because we have chosen how we wanted. We follow the landmark 4.
- In order that we do not must complicate the design, we have taken out of given line-right only semi-right positive. It is determined by the origin (+O) and by the point U. We will see how much (points) are between origin (+O) and point U, also many points are between infinitely large (+I) and point U. They are called equipotenta lots of. To do this we use the function y = F (x) = 1 / x; (landmark 4). This function (F), make a transformation named inversion. Thus a point (P) with coordinate x that belongs to the interval (OU] corresponds to a single point (P') with coordinate 1 / x that belongs the interval [U, I). For example: For the point (P) with coordinated + 0,125 corepunde a point (P') with coordinated 1 / 0,125 = +8. This function is invertible x = F–1(y) = 1 / y. Therefore, we infer that the function is and bijective. This means that the points belonging to the interval (+ OU] corespond one at one with the points that belong to the interval [UI). So, we have inferred that these sets of points are equipotent. It is obvious that the point "U" corresponds to himself. But with what (point) corresponds the origin (+O, infinitely small)? The origin (+ O) corresponds with the point +I. This point is the large infinitely. This the explanation ask passage it at limit:
- so, for point +O correspond the point +I. For that matter, and vice versa:
- 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 the topical infinitely), but we can not see the point +I (it is called the potential infinity). But this is only a human illusion, because we are very tiny compared to the infinitely large. We can not see than locally, around our (point ±O). We have a perspective (an horizon) of a frog shortsighted. To see and the infinitely large we must have a perspective (an horizon) of eagle. For this we will divide unevenly semi-axis (the units will be variable ) and they are not equal as we do locally (here, on our the planet, in around us). See the landmark 5.
- In order not to complicate the understanding of the background we will not go into details of this unequal divisions. We will choose an appropriate function which (for a Cartesian coordinate for axles) will indicate the length of the segment that will take. Function chosen is a transformation by translational composed with a symmetry to the axis of function of echilatere hyperbola. Now, we will see and the infinite large (+I), because the points are crowded in around him +O and +I. With as points are the farther, with so the scaling function has brought them closer towards point +I. We observe that (+ O + I) is an open segment, because the 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 of on right (landmark 6). Now it is simple: Also, all points of negative semi-axle are equipotent with those of positive semi-axle. This we infer from the symmetry given by the function y = F(x) = –x. We believe that the Figure 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. Another is –I = –?. It is large infinitely from negative semi-axle. But we will infer that they are identical. The correspondent by inversion for point +I is point +O. The correspondent by inversion for point –I is point –O. But how +O = –O, then +I = –I.
- We should see that infinitely large is unapproachable. Infinitely small is likewise unapproachable. These knowledge are imposible for human, because they do not exist. Astronomy sees that nothing exist away more than 13.73 billion years light.
- We are puting the question: If two semi-right (+ O; +I) and (–O; –I) have two common points, then they coincide. But we know well from the geometric intuition that these semi-right opposite (+ O; +I) and (–O; –I) "not" coincide. The reason is that in eagle perspective what we call right-line is actually a closed curve (ellipse, circle etc.). We refer at the landmark 7 from "Figure
- Also, any point on the right could be chosen as the origin or could be diametrically opposite point of origin. Moreover: If we choose another point as the origin (P) on the right, then its opposite would become infinitely large, while the former infinitely large will become a trivial point on right. Thus, we deduce that the infinite (large or small) is referentially dependent. In other words: These infinites were created by numbers real (those which give the coordinates for those points). But real numbers are created by passing to boundary at small-infinite of strings of rational-numbers. But this is a vicious circle. So, the infinites are introduced in physics by a mistake of mathematics. So, they are not objective.
- In conclusion: The mathematics consider that large and small infinites there are. This mistake remained from the Middle Ages, because they knew not physics for micro-cosmos and modern astronomy. But now, Planck showed that they do not exist, because everything is finite. We must to believe physics, because the physics is using the theoretical deduction as mathematics, but also, experimental verification, scientific observations and practical applications.
- Planck showed previously that the only reality (natural and objective)is that on the right is a finite lots of points.
- We admite (astronomers concluded) that the Universe would be a giant sphere with a radius of 13.73 billion years-light. This radius has = 13,73 billion years-light = 13,73 billion years-light × 3×10^+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 / L(incex P) = 2 × 1,3 × 10^+26 m / 1,6160 × 10^-35 m = 2 × 8 × 10^60 = 1,6 × 10^61. So, the lots of natural numbers = maximum lots of points of the right-line. So, they are finished. If we will choose an origin on the right and a positive meaning, then it is also the lots of integers numbers finite = (? 8 × 10^60). These are natural cartesian coordinates for points on the right.
- This number 2 × 8 × 10^60 L(index P) = 2 × 13,73 bilions yars-light = 2 × 1,3 × 10^+26 m is true infinitely large physical. The number 1 L(incex P) = 1,6160 × 10^-35 m is (true) small infinitely physical. So mathematics has created a beautiful story of science fiction.
- We can now easily generalize this infinites at the physical plane, at the entire three-dimensional space and at all existing physical quantities.
- For example: We will demonstrate for the second degree one-dimensional spaces. Hyperboles and geometric-parables do not exist because they have ramifications at infinity. They are an illusion given the local perspective. We shall prove that exist only ellipses. See Figure
- We consider a spherical surface passing through the planet and through a point on the edge of the Universe (therefore, at a distance of 8 × 10^60 L(index P) = 13,73 LY = 1,3 × 10^+26 m). We will delimit a spherical calotte with the pole on the planet. Calotte is the human horizon for direct eyesight (less that 500 km, even in the plane).
- [1] Inside this calotte we will draw an ellipse. It exists, because we see it in full.
- [2] Now we will draw an ellipse with only the tops into the limit human horizon. Now, we will perceive the 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 the horizon, then 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 the planet near of its surface. Now, the human horizon of direct vision is a sphere with a radius of about 500 Km. We shall 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 (tops) into our 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 the uman horizon. We see these two pairs of tops as follows: We will intersect the hyperboloid with the plane z = 0. The 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 pair.
- Thus, we can continue to eliminate this mistake and from mathematics as they have already done our colleagues in physics.
- Something similar is happening and with all line-right from beam (eg: In Figure
- Therefore, we have made a bijective correspondence between points on semi-right elected “[OUI” and all semi-right of the beam (D). So, any point on the semi-right [OUI corresponds to a semi-straight of beam (“one” to “one”). It follows that: Points O and I correspond with semi-right [DO (infinitely small for beam) and [DI (which is infinitely large for beam).
- But we will study how the physics sees the same problem: We will use figure
- In conclusion: The phantom named "infinite mathematical" was expelled by physicists and out of the beam. So physicists have eliminated (everywhere) the infinitely out of physical. But if mathematicians (even themselves) would eliminate their the infinite, then it would have been better, because this infects all the math. We see how this do wrong: topology, analysis, etc. Infinite corrupts absolutely throughout science, because this came logically incorrect in mathematics (without theorem of existence, without existence theorem 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:
arghirescu_alexandru@yahoo.com
