The history of the origin of zero is brief. Zero or zero, numerology sign and its meaning

Very few people understand the essence of electricity. Concepts such as “electric current”, “voltage”, “phase” and “zero” are a dark forest for most, although we encounter them every day. Let's get a grain of useful knowledge and figure out what phase and zero are in electricity. To teach electricity from scratch, we need to understand the fundamental concepts. We are primarily interested in electric current and electric charge.

Electric current and electric charge

Electric charge is a physical scalar quantity that determines the ability of bodies to be a source of electromagnetic fields. The carrier of the smallest or elementary electric charge is the electron. Its charge is approximately -1.6 to 10 to the minus nineteenth power of Coulomb.

Electron charge is the minimum electrical charge (quantum, portion of charge) that occurs in nature in free, long-lived particles.

Charges are conventionally divided into positive and negative. For example, if we rub an ebonite stick on wool, it will acquire a negative electrical charge (excess electrons that were captured by the atoms of the stick upon contact with the wool).

Static electricity on the hair has the same nature, only in this case the charge is positive (the hair loses electrons).

The main type of alternating current is sinusoidal current . This is a current that first increases in one direction, reaches a maximum (amplitude), begins to decrease, at some point becomes equal to zero and increases again, but in a different direction.


Directly about the mysterious phase and zero

We have all heard about phase, three phases, zero and grounding.

The simplest case of an electrical circuit is single phase circuit . It only has three wires. Through one of the wires the current flows to the consumer (let it be an iron or hair dryer), and through the other it returns back. The third wire in a single-phase network is earth (or grounding).

The ground wire does not carry a load, but serves as a fuse. In case something gets out of control, grounding helps prevent electric shock. This wire carries excess electricity or “drains” into the ground.

The wire through which current flows to the device is called phase , and the wire through which the current returns is zero.

So, why do we need zero in electricity? Yes, for the same thing as the phase! The current flows through the phase wire to the consumer, and through the neutral wire it is discharged in the opposite direction. The network through which alternating current is distributed is three-phase. It consists of three phase wires and one return.

It is through this network that the current flows to our apartments. Approaching directly to the consumer (apartments), the current is divided into phases, and each phase is given a zero. The frequency of changing the direction of current in the CIS countries is 50 Hz.

Different countries have different network voltage and frequency standards. For example, a typical household outlet in the United States supplies alternating current with a voltage of 100-127 Volts and a frequency of 60 Hertz.

The phase and neutral wires should not be confused. Otherwise, you can cause a short circuit in the circuit. To prevent this from happening and to prevent you from confusing anything, the wires have acquired different colors.

What color are phase and zero indicated in electricity? Zero is usually blue or cyan, and phase is white, black or brown. The ground wire also has its own color - yellow-green.


So, today we learned what the concepts of “phase” and “zero” mean in electricity. We will be simply happy if this information was new and interesting for someone. Now, when you hear something about electricity, phase, zero and ground, you will already know what we are talking about. Finally, we remind you that if you suddenly need to calculate a three-phase AC circuit, you can safely contact student service. With the help of our specialists, even the wildest and most difficult task will be up to you.

The need for counting became obvious to man from the very beginning of the formation of primitive society. Their own numerical systems, with specific digital designations, were formed in all isolated centers of civilization: in Egypt and Ancient Babylon, in China and India, among the South American Indians and in ancient Greece. Mathematics has gone from the simplest counting of objects to solving the most complex theorems of topology. Moreover, the history of the number zero covers only a tiny part of this period.

Numbers and figures

From the Latin nullis (“no”) comes the word denoting one of the most important mathematical concepts. It includes not only a symbol - a number that helps to keep count and write down mathematical operations. It's a whole concept. The absence of any quantity, emptiness, beginning and infinity - the philosophical attitude towards these concepts was different in different eras, in different worldview systems.

Positional number systems

In prehistoric times, fingers and toes helped with calculations. The division of numbers into fives and tens, the origin of the decimal is connected precisely with this. Later, to facilitate these operations, notches on wood and animal bones, notches on stones, and pebbles were used. shells and other small items. Each such element represents a specific number. The most practical numerical models have a similar nature. Such systems are called positional - the meaning of digits when writing numbers is determined by their position or digit.

An example of a system that is opposite in approach and is still used today is the method of writing numbers that has come down from the times of Ancient Rome. It uses letters to denote units, tens, hundreds

Abacus

The counting board, consisting of recesses corresponding to certain categories into which pebbles or beads are placed, is familiar to the cultures of different peoples and eras. Other varieties of abacus are also known - ropes with knots or cords with beads. The next step in the development of such a device was the abacus, which was used before the advent of calculators.

The history of the number zero is the process of the emergence of a mathematical concept and the beginning of the use of the symbol denoting it. Both the abacus and the abacus are, in a sense, a means of visualization. An empty space in the corresponding recess or a missing knuckle on the abacus made the abstract concept of zero visual. The symbol denoting it first appeared among the mathematicians and astronomers of Ancient Babylon.

Babylonian sign of the void

The civilization born between the Tigris and Euphrates rivers adopted a numerical system inherited from the ancient Sumerians. It was positional - the meaning of the numbers depended on their position relative to other numbers. Developed 4-5 thousand years BC. e., it was built on the number 60. The mathematical calculations used by ancient Babylonian engineers and astronomers therefore looked quite cumbersome and inconvenient. To successfully operate with numbers, it was necessary to remember by heart or have in front of your eyes the results of multiplying all numbers from 1 to 60.

The number zero, or the sign adopted by the Babylonians to indicate rank, looked like two wedges or arrows placed at an angle. This symbol was an integral part of a number and did not participate in arithmetic operations - it was impossible to add or multiply by it.

Overseas zero

Regardless of the mathematicians of Mesopotamia, the Indians of Central America - the Mayans and Incas - introduced their zero into use. What both number systems had in common was that they did not develop the idea of ​​zero as a number.

Ancient American civilization left the world many achievements in the intellectual sphere. The complex calendar systems of the Mayans and Incas are the result of centuries of experience in astronomical observations and complex mathematical calculations. But never in their equations was the number zero present as a number influencing the result of mathematical operations.

Antique look

Their main legacy was their achievements in geometry and astronomy. Numbers in their representation are segments with a beginning, an end and a certain length. Zero is a number that has no practical value in this case. A segment with zero length had no meaning in ancient mathematics and philosophy.

One of the main tenets of Aristotle's teachings is the phrase Natura abhorret vacuum - "Nature abhors a vacuum." Infinity, nothingness, non-existence - these categories did not fit into the ancient universe. Therefore, the modern meaning of the question “what number is 0” was unattainable for Archimedes, Pythagoras or Euclid, although a symbol similar to zero is found in the tables of the great astronomer Ptolemy. He wrote the letter "Omicron" (the first letter in the word οὐδέν - "nothing") in empty cells.

The birthplace of zero is India

What did Indian mathematicians invent? Mahavira (850), Brahmagupta (1114), Aryabhata (476) are the authors of treatises in which the modern system of recording numbers and the rules of basic arithmetic operations largely took shape. Historians believe that the decimal number system was borrowed by the Indians from the Chinese, and its positional character from the Babylonians. It is believed that the symbol of zero was also borrowed by the Indians from the works of Ptolemy.

The first mathematician to formulate a complete numerical system, which still remains unchanged and serves the majority of humanity, was Khwarizmi Muhammad ben Musa (787-850), who lived in Baghdad. His Book of Indian Counting details the nine Arabic numerals and answers the question, “Is 0 a number?” The mention of zero in this book is considered the first. The Latin translation of this work became widely known in Europe in the 12th century and marked the beginning of the spread of Eastern mathematical knowledge.

Unlike Europeans, Eastern philosophers were awed by eternity. Therefore, zero in the equations of ancient Indian scientists finally became not only a symbol of the absence of units in the corresponding digit, but also a natural number influencing the result of calculations. Adding zero, multiplying by 0 - all this acquired the meaning of meaningful mathematical operations.

The very writing of numbers from 1 to 0 acquired its final form also thanks to ancient Indian mathematical treatises, and those symbols that are usually called Arabic in Europe are called Indian by the Arabs themselves.

The history of the number “zero” is reflected in the etymology of basic mathematical terms. The word “digit” has Arabic roots and comes from the word “al-sifr”, which means “empty, zero”. The English “zero” vaguely resembles “zephyr” - the wind from the east - it was from the East that a finally formed, rational and convenient numerical system came to Europe.

in Europe

One of the main European propagandists of the Arabic digital system was the famous Italian mathematician Leonardo Fibonacci. His work “The Book of Abacus” (1202) introduced European scientists to the symbols and rules with which the Arabs wrote down mathematical operations. The first to appreciate the convenience and rationality of the Eastern mathematical model were those who were accustomed to daily handling of numbers - bankers and traders. They quickly adopted the number system and writing of numbers from Arab merchants. But this knowledge became firmly integrated into the scientific practice of Europe only after 4 centuries, replacing the ancient system adopted by European mathematicians.

Zero gained importance with the introduction into scientific use of the rectangular coordinate system, proposed in the 17th century by Rene Descartes. Zero, located in the center, has acquired the meaning of a visible and visually understandable reference point for the three coordinate axes.

In Russia, zero was introduced into practice through the efforts of Leonty Magnitsky, the author of the famous textbook “Arithmetic, that is, the science of numbers” (1703).

Properties of zero

Zero, which demarcates positive and negative numbers, has unique mathematical properties. This is an even, unsigned natural integer. Adding with zero and subtracting zero has no effect on the number, but multiplying by 0 gives zero. Division by zero is considered a meaningless operation that, if performed in a computer program, could cause significant harm to the system.

It was in the attempt to divide by 0 that the meaning of the failure in the computer system of the US Navy cruiser Yorktown turned out to be, which occurred in the fall of 1997 and led to the unauthorized shutdown of the propulsion system. An incorrect attitude to the number meaning “nothing” turned a powerful warship into a helpless, motionless target.

The significance of this number increased significantly with the development of science. Zero appears in areas not only purely mathematical. The hearing threshold in acoustics is taken to be 0. What number is at the beginning of the scale of many measuring instruments is known to schoolchildren: 0 on the Celsius scale is the freezing point of water, the beginning of longitude is the prime meridian, etc.

Binary notation, which served as the basis for the creation of modern computing devices, is a positional number system with a base of two. This means that all data entered into computer systems is encoded using a combination of two characters - one and zero.

The role of computers in the modern world is becoming decisive for all aspects of life, which means that the history of the number zero, without which their appearance would have been impossible, continues.

There is a special attitude towards the number 0 in numerology. All number values ​​are divided into two large groups:

  1. Positive, carrying a positive beginning.
  2. Negative, negatively affecting fate.

The number 0 is the beginning of infinity, a symbol of purity and freedom, the root cause of everything that can happen, the starting point.

It is from this understanding that all positive properties come. Positive meanings of numbers in numerology:

Negative values

Behind the number 0 lies its dual essence. He can begin and end, bring down to emptiness, raise to the top. The number pulls you into its middle.

It is not for nothing that the most terrible natural phenomena are similar in form to it. Looking inside, you may not return to reality. Negative values:

Features of zero in numerology

Spiritual numerology gives its own interpretation of the number: time freezes in it.

Movements in any sense stop.

Everything that is in the space around is in a state of peace and silence.

But this does not mean death or oblivion.

Internal energy is preparing to exit.

Some scientists believe that zero is the junction of numerology and esotericism.

United contrast positions

The number zero stands on the boundary of concepts. That is why the correct guidance of the fate line often depends on the person.

Such positions are dangerous. They can bring grief to weak people, confidence and happiness to strong people. What contradictions does it hide?

  • birth - death;
  • lie - truth;
  • secret - reality;
  • light - darkness.

There is a very thin line between contrasting positions; it can break at any moment. From one side, light, they imperceptibly move to the other, dark. All signs of fate initially come from zero, as from a point from which you can turn in any direction.

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  • The number ten signifies completeness. It consists of 2 digits. One is the divine line, leadership and success. Zero is neutral, balances the power of “1”. Let's consider the meaning of ten in fate...
  • Simply put, these are vegetables cooked in water according to a special recipe. I will consider two initial components (vegetable salad and water) and the finished result - borscht. Geometrically, it can be thought of as a rectangle, with one side representing lettuce and the other side representing water. The sum of these two sides will indicate borscht. The diagonal and area of ​​such a “borscht” rectangle are purely mathematical concepts and are never used in borscht recipes.


    How do lettuce and water turn into borscht from a mathematical point of view? How can the sum of two line segments become trigonometry? To understand this, we need linear angular functions.


    You won't find anything about linear angular functions in math textbooks. But without them there can be no mathematics. The laws of mathematics, like the laws of nature, work regardless of whether we know about their existence or not.

    Linear angular functions are addition laws. See how algebra turns into geometry and geometry turns into trigonometry.

    Is it possible to do without linear angular functions? It’s possible, because mathematicians still manage without them. The trick of mathematicians is that they always tell us only about those problems that they themselves know how to solve, and never talk about those problems that they cannot solve. Look. If we know the result of addition and one term, we use subtraction to find the other term. All. We don’t know other problems and we don’t know how to solve them. What should we do if we only know the result of the addition and do not know both terms? In this case, the result of the addition must be decomposed into two terms using linear angular functions. Next, we ourselves choose what one term can be, and linear angular functions show what the second term should be so that the result of the addition is exactly what we need. There can be an infinite number of such pairs of terms. In everyday life, we get along just fine without decomposing the sum; subtraction is enough for us. But in scientific research into the laws of nature, decomposing a sum into its components can be very useful.

    Another law of addition that mathematicians don't like to talk about (another of their tricks) requires that the terms have the same units of measurement. For salad, water, and borscht, these could be units of weight, volume, value, or unit of measure.

    The figure shows two levels of difference for mathematical . The first level is the differences in the field of numbers, which are indicated a, b, c. This is what mathematicians do. The second level is the differences in the field of units of measurement, which are shown in square brackets and indicated by the letter U. This is what physicists do. We can understand the third level - differences in the area of ​​​​the objects being described. Different objects can have the same number of identical units of measurement. How important this is, we can see in the example of borscht trigonometry. If we add subscripts to the same unit designation for different objects, we can say exactly what mathematical quantity describes a particular object and how it changes over time or due to our actions. Letter W I will designate water with a letter S I'll designate the salad with a letter B- borsch. This is what linear angular functions for borscht will look like.

    If we take some part of the water and some part of the salad, together they will turn into one portion of borscht. Here I suggest you take a little break from borscht and remember your distant childhood. Remember how we were taught to put bunnies and ducks together? It was necessary to find how many animals there would be. What were we taught to do then? We were taught to separate units of measurement from numbers and add numbers. Yes, any one number can be added to any other number. This is a direct path to the autism of modern mathematics - we do it incomprehensibly what, incomprehensibly why, and very poorly understand how this relates to reality, because of the three levels of difference, mathematicians operate with only one. It would be more correct to learn how to move from one unit of measurement to another.

    Bunnies, ducks, and little animals can be counted in pieces. One common unit of measurement for different objects allows us to add them together. This is a children's version of the problem. Let's look at a similar problem for adults. What do you get when you add bunnies and money? There are two possible solutions here.

    First option. We determine the market value of the bunnies and add it to the available amount of money. We got the total value of our wealth in monetary terms.

    Second option. You can add the number of bunnies to the number of banknotes we have. We will receive the amount of movable property in pieces.

    As you can see, the same addition law allows you to get different results. It all depends on what exactly we want to know.

    But let's get back to our borscht. Now we can see what will happen for different angle values ​​of linear angular functions.

    The angle is zero. We have salad, but no water. We can't cook borscht. The amount of borscht is also zero. This does not mean at all that zero borscht is equal to zero water. There can be zero borscht with zero salad (right angle).


    For me personally, this is the main mathematical proof of the fact that . Zero does not change the number when added. This happens because addition itself is impossible if there is only one term and the second term is missing. You can feel about this as you like, but remember - all mathematical operations with zero were invented by mathematicians themselves, so throw away your logic and stupidly cram the definitions invented by mathematicians: “division by zero is impossible”, “any number multiplied by zero equals zero” , “beyond the puncture point zero” and other nonsense. It is enough to remember once that zero is not a number, and you will never again have a question whether zero is a natural number or not, because such a question loses all meaning: how can something that is not a number be considered a number? It's like asking what color an invisible color should be classified as. Adding a zero to a number is the same as painting with paint that is not there. We waved a dry brush and told everyone that “we painted.” But I digress a little.

    The angle is greater than zero but less than forty-five degrees. We have a lot of lettuce, but not enough water. As a result, we will get thick borscht.

    The angle is forty-five degrees. We have equal quantities of water and salad. This is the perfect borscht (forgive me, chefs, it's just math).

    The angle is greater than forty-five degrees, but less than ninety degrees. We have a lot of water and little salad. You will get liquid borscht.

    Right angle. We have water. All that remains of the salad are memories, as we continue to measure the angle from the line that once marked the salad. We can't cook borscht. The amount of borscht is zero. In this case, hold on and drink water while you have it)))

    Here. Something like this. I can tell other stories here that would be more than appropriate here.

    Two friends had their shares in a common business. After killing one of them, everything went to the other.

    The emergence of mathematics on our planet.

    All these stories are told in the language of mathematics using linear angular functions. Some other time I will show you the real place of these functions in the structure of mathematics. In the meantime, let's return to borscht trigonometry and consider projections.

    Saturday, October 26, 2019

    Wednesday, August 7, 2019

    Concluding the conversation about, we need to consider an infinite set. The point is that the concept of “infinity” affects mathematicians like a boa constrictor affects a rabbit. The trembling horror of infinity deprives mathematicians of common sense. Here's an example:

    The original source is located. Alpha stands for real number. The equal sign in the above expressions indicates that if you add a number or infinity to infinity, nothing will change, the result will be the same infinity. If we take the infinite set of natural numbers as an example, then the considered examples can be represented in the following form:

    To clearly prove that they were right, mathematicians came up with many different methods. Personally, I look at all these methods as shamans dancing with tambourines. Essentially, they all boil down to the fact that either some of the rooms are unoccupied and new guests are moving in, or that some of the visitors are thrown out into the corridor to make room for guests (very humanly). I presented my view on such decisions in the form of a fantasy story about the Blonde. What is my reasoning based on? Relocating an infinite number of visitors takes an infinite amount of time. After we have vacated the first room for a guest, one of the visitors will always walk along the corridor from his room to the next one until the end of time. Of course, the time factor can be stupidly ignored, but this will be in the category of “no law is written for fools.” It all depends on what we are doing: adjusting reality to mathematical theories or vice versa.

    What is an “endless hotel”? An infinite hotel is a hotel that always has any number of empty beds, regardless of how many rooms are occupied. If all the rooms in the endless "visitor" corridor are occupied, there is another endless corridor with "guest" rooms. There will be an infinite number of such corridors. Moreover, the “infinite hotel” has an infinite number of floors in an infinite number of buildings on an infinite number of planets in an infinite number of universes created by an infinite number of Gods. Mathematicians are not able to distance themselves from banal everyday problems: there is always only one God-Allah-Buddha, there is only one hotel, there is only one corridor. So mathematicians are trying to juggle the serial numbers of hotel rooms, convincing us that it is possible to “shove in the impossible.”

    I will demonstrate the logic of my reasoning to you using the example of an infinite set of natural numbers. First you need to answer a very simple question: how many sets of natural numbers are there - one or many? There is no correct answer to this question, since we invented numbers ourselves; numbers do not exist in Nature. Yes, Nature is great at counting, but for this she uses other mathematical tools that are not familiar to us. I’ll tell you what Nature thinks another time. Since we invented numbers, we ourselves will decide how many sets of natural numbers there are. Let's consider both options, as befits real scientists.

    Option one. “Let us be given” one single set of natural numbers, which lies serenely on the shelf. We take this set from the shelf. That's it, there are no other natural numbers left on the shelf and nowhere to take them. We cannot add one to this set, since we already have it. What if you really want to? No problem. We can take one from the set we have already taken and return it to the shelf. After that, we can take one from the shelf and add it to what we have left. As a result, we will again get an infinite set of natural numbers. You can write down all our manipulations like this:

    I wrote down the actions in algebraic notation and in set theory notation, with a detailed listing of the elements of the set. The subscript indicates that we have one and only set of natural numbers. It turns out that the set of natural numbers will remain unchanged only if one is subtracted from it and the same unit is added.

    Option two. We have many different infinite sets of natural numbers on our shelf. I emphasize - DIFFERENT, despite the fact that they are practically indistinguishable. Let's take one of these sets. Then we take one from another set of natural numbers and add it to the set we have already taken. We can even add two sets of natural numbers. This is what we get:

    The subscripts "one" and "two" indicate that these elements belonged to different sets. Yes, if you add one to an infinite set, the result will also be an infinite set, but it will not be the same as the original set. If you add another infinite set to one infinite set, the result is a new infinite set consisting of the elements of the first two sets.

    The set of natural numbers is used for counting in the same way as a ruler is for measuring. Now imagine that you added one centimeter to the ruler. This will be a different line, not equal to the original one.

    You can accept or not accept my reasoning - it is your own business. But if you ever encounter mathematical problems, think about whether you are following the path of false reasoning trodden by generations of mathematicians. After all, studying mathematics, first of all, forms a stable stereotype of thinking in us, and only then adds to our mental abilities (or, conversely, deprives us of free-thinking).

    pozg.ru

    Sunday, August 4, 2019

    I was finishing a postscript to an article about and saw this wonderful text on Wikipedia:

    We read: "... the rich theoretical basis of the mathematics of Babylon did not have a holistic character and was reduced to a set of disparate techniques, devoid of a common system and evidence base."

    Wow! How smart we are and how well we can see the shortcomings of others. Is it difficult for us to look at modern mathematics in the same context? Slightly paraphrasing the above text, I personally got the following:

    The rich theoretical basis of modern mathematics is not holistic in nature and is reduced to a set of disparate sections, devoid of a common system and evidence base.

    I won’t go far to confirm my words - it has a language and conventions that are different from the language and conventions of many other branches of mathematics. The same names in different branches of mathematics can have different meanings. I want to devote a whole series of publications to the most obvious mistakes of modern mathematics. See you soon.

    Saturday, August 3, 2019

    How to divide a set into subsets? To do this, you need to enter a new unit of measurement that is present in some of the elements of the selected set. Let's look at an example.

    May we have plenty A consisting of four people. This set is formed on the basis of “people.” Let us denote the elements of this set by the letter A, the subscript with a number will indicate the serial number of each person in this set. Let's introduce a new unit of measurement "gender" and denote it by the letter b. Since sexual characteristics are inherent in all people, we multiply each element of the set A based on gender b. Notice that our set of “people” has now become a set of “people with gender characteristics.” After this we can divide the sexual characteristics into male bm and women's bw sexual characteristics. Now we can apply a mathematical filter: we select one of these sexual characteristics, no matter which one - male or female. If a person has it, then we multiply it by one, if there is no such sign, we multiply it by zero. And then we use regular school mathematics. Look what happened.

    After multiplication, reduction and rearrangement, we ended up with two subsets: the subset of men Bm and a subset of women Bw. Mathematicians reason in approximately the same way when they apply set theory in practice. But they don’t tell us the details, but give us the finished result - “a lot of people consist of a subset of men and a subset of women.” Naturally, you may have a question: how correctly has the mathematics been applied in the transformations outlined above? I dare to assure you that, in essence, the transformations were done correctly; it is enough to know the mathematical basis of arithmetic, Boolean algebra and other branches of mathematics. What it is? Some other time I will tell you about this.

    As for supersets, you can combine two sets into one superset by selecting the unit of measurement present in the elements of these two sets.

    As you can see, units of measurement and ordinary mathematics make set theory a relic of the past. A sign that all is not well with set theory is that mathematicians have come up with their own language and notation for set theory. Mathematicians acted as shamans once did. Only shamans know how to “correctly” apply their “knowledge.” They teach us this “knowledge”.

    In conclusion, I want to show you how mathematicians manipulate .

    Monday, January 7, 2019

    In the fifth century BC, the ancient Greek philosopher Zeno of Elea formulated his famous aporias, the most famous of which is the “Achilles and the Tortoise” aporia. Here's what it sounds like:

    Let's say Achilles runs ten times faster than the tortoise and is a thousand steps behind it. During the time it takes Achilles to run this distance, the tortoise will crawl a hundred steps in the same direction. When Achilles runs a hundred steps, the tortoise crawls another ten steps, and so on. The process will continue ad infinitum, Achilles will never catch up with the tortoise.

    This reasoning became a logical shock for all subsequent generations. Aristotle, Diogenes, Kant, Hegel, Hilbert... They all considered Zeno's aporia in one way or another. The shock was so strong that " ... discussions continue to this day; the scientific community has not yet been able to come to a common opinion on the essence of paradoxes ... mathematical analysis, set theory, new physical and philosophical approaches were involved in the study of the issue; none of them became a generally accepted solution to the problem..."[Wikipedia, "Zeno's Aporia". Everyone understands that they are being fooled, but no one understands what the deception consists of.

    From a mathematical point of view, Zeno in his aporia clearly demonstrated the transition from quantity to . This transition implies application instead of permanent ones. As far as I understand, the mathematical apparatus for using variable units of measurement has either not yet been developed, or it has not been applied to Zeno’s aporia. Applying our usual logic leads us into a trap. We, due to the inertia of thinking, apply constant units of time to the reciprocal value. From a physical point of view, this looks like time slowing down until it stops completely at the moment when Achilles catches up with the turtle. If time stops, Achilles can no longer outrun the tortoise.

    If we turn our usual logic around, everything falls into place. Achilles runs at a constant speed. Each subsequent segment of his path is ten times shorter than the previous one. Accordingly, the time spent on overcoming it is ten times less than the previous one. If we apply the concept of “infinity” in this situation, then it would be correct to say “Achilles will catch up with the turtle infinitely quickly.”

    How to avoid this logical trap? Remain in constant units of time and do not switch to reciprocal units. In Zeno's language it looks like this:

    In the time it takes Achilles to run a thousand steps, the tortoise will crawl a hundred steps in the same direction. During the next time interval equal to the first, Achilles will run another thousand steps, and the tortoise will crawl a hundred steps. Now Achilles is eight hundred steps ahead of the tortoise.

    This approach adequately describes reality without any logical paradoxes. But this is not a complete solution to the problem. Einstein’s statement about the irresistibility of the speed of light is very similar to Zeno’s aporia “Achilles and the Tortoise”. We still have to study, rethink and solve this problem. And the solution must be sought not in infinitely large numbers, but in units of measurement.

    Another interesting aporia of Zeno tells about a flying arrow:

    A flying arrow is motionless, since at every moment of time it is at rest, and since it is at rest at every moment of time, it is always at rest.

    In this aporia, the logical paradox is overcome very simply - it is enough to clarify that at each moment of time a flying arrow is at rest at different points in space, which, in fact, is motion. Another point needs to be noted here. From one photograph of a car on the road it is impossible to determine either the fact of its movement or the distance to it. To determine whether a car is moving, you need two photographs taken from the same point at different points in time, but you cannot determine the distance from them. To determine the distance to a car, you need two photographs taken from different points in space at one point in time, but from them you cannot determine the fact of movement (of course, you still need additional data for calculations, trigonometry will help you). What I want to draw special attention to is that two points in time and two points in space are different things that should not be confused, because they provide different opportunities for research.
    I'll show you the process with an example. We select the “red solid in a pimple” - this is our “whole”. At the same time, we see that these things are with a bow, and there are without a bow. After that, we select part of the “whole” and form a set “with a bow”. This is how shamans get their food by tying their set theory to reality.

    Now let's do a little trick. Let’s take “solid with a pimple with a bow” and combine these “wholes” according to color, selecting the red elements. We got a lot of "red". Now the final question: are the resulting sets “with a bow” and “red” the same set or two different sets? Only shamans know the answer. More precisely, they themselves do not know anything, but as they say, so it will be.

    This simple example shows that set theory is completely useless when it comes to reality. What's the secret? We formed a set of "red solid with a pimple and a bow." The formation took place in four different units of measurement: color (red), strength (solid), roughness (pimply), decoration (with a bow). Only a set of units of measurement allows us to adequately describe real objects in the language of mathematics. This is what it looks like.

    The letter "a" with different indices denotes different units of measurement. The units of measurement by which the “whole” is distinguished at the preliminary stage are highlighted in brackets. The unit of measurement by which the set is formed is taken out of brackets. The last line shows the final result - an element of the set. As you can see, if we use units of measurement to form a set, then the result does not depend on the order of our actions. And this is mathematics, and not the dancing of shamans with tambourines. Shamans can “intuitively” come to the same result, arguing that it is “obvious,” because units of measurement are not part of their “scientific” arsenal.

    Using units of measurement, it is very easy to split one set or combine several sets into one superset. Let's take a closer look at the algebra of this process.

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    Just think, zero! Nothing! What if you think about it? If we didn’t have zero now, there would be no computers, no television, no mobile communications... no digital technologies! What can I say, we wouldn’t be able to multiply two two-digit numbers. Zero is a great invention of mankind and the cornerstone of our number system. Zero is worth talking about.

    The number "nothing"

    The life of the number and the number “zero” began from the moment when people realized the need to designate “nothing” with a specific number. Before this, the collective mind believed that if there is nothing, there is no need to write anything down. But the geniuses of mankind in different parts of the world realized that zero is vital. These were the Mayan Indians in America, someone came up with a sign to indicate zero in Ancient Babylon, and someone in China.

    And the sages originally from Hindustan designated zero with the sign of an elongated circle, which is familiar to us.

    The word “Zero” (Zero) comes to us from the Latin “Nulus” - none.

    With zero everything is in its place!

    With the advent of the designation zero, everything literally took its place. A convenient and practical positional number system has appeared, in which the value of a digit depends on its place in the number record, that is, on its position. The use of the number zero made it possible not to introduce new signs for writing large numbers. An elegant system has emerged for writing any number using just ten digits. Now no one will confuse the numbers 15, 150, 105 or 15000.

    Arithmetic properties of zero

    Since zero is a number, it has properties. If you add zero to any number, the number does not change. If you subtract zero from any number, the number will not change (add or subtract, but zero remains nothing!). If we multiply zero by a number, we get zero, since we took the number zero times. Zero divided by any number gives zero. This is clear, we divide zero into any number of parts - we get zero!

    Now let's try to divide the number by zero. Is it possible to divide a number into zero parts? How then, from zero parts, can we put together again what we divided? To avoid such difficulties, division by zero was banned. You can't divide by zero!

    Zero - the beginning of the journey

    If you are driving along the highway, then along the way you will come across kilometer posts with marks: 20 km., 30 km. etc. These are indicators of the distance from the main post office of the city from which you left. The main post office in the city is considered the beginning of the journey, its zero mark.

    In some cities, the zero mark or the beginning of the path are specially installed signs with the mark “Beginning of roads. Zero kilometer). For example, such a sign was installed in the center of modern Minsk (the capital of Belarus), on Oktyabrskaya Square.

    And in the capital of Hungary, Budapest, at the site of the zero kilometer, the beginning of all roads, a monument to Zero was erected. This is the only monument to digital.

    Railways in the Russian Federation are counted from Moscow (Moscow is the beginning of the route, the zero mark). The Oktyabrskaya Railway starts its countdown from St. Petersburg (in this case, St. Petersburg is the zero mark).

    The calculation of the Earth's meridians to determine geographic coordinates is carried out from Greenwich (prime meridian).

    Zero - the beginning of time

    The beginning of all time... Where is it? If this beginning is the moment of the emergence of the Universe, then scientists are still arguing when this happened... If it is the time of the emergence of life on Earth, then it is also difficult to decide...

    Then people agreed on a conditional beginning of time, tying it to a specific event. As you may have guessed, this event is the Nativity of Christ. It is from the Nativity of Christ that we count our time, we count down our time. We consider the Nativity of Christ to be the zero point on the time line. Everything that happened before the Nativity of Christ was before our era; and everything that happened later was in our era.

    Each person has their own relationship with zero. But no one wants to have zero income, zero success, zero relationships and zero knowledge. You can improve your knowledge of mathematics by studying articles in the section.

    However, zero is not always such a thing, if you remember that it is “zero” - three out of forty casino cells with the designation zero - that brings fabulous profits to the gambling business!

    

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