Zero. This important nothing

What does zero mean? In fact, zero (zero) was not even considered a number until almost the 18th century, and the history of the appearance of zero in many number systems of different countries and cultures is very different, and not only in the era of its “birth”, but also in its graphic representation. For example, while the ancient Egyptians and Sumerians already used this sign in their calculations, depicting it with a special hieroglyph, the ancient Greeks did not have such a sign in their number system.

What does zero mean in numerology

Zero symbolizes the Absolute, connecting Matter with Spirit. This definition of symbolism arose from the potential ability to separate any number from a whole.

Zero in the manifestation of different aspects

By adding a zero to any of the numbers on the right side, we get a number multiplied by 10 times. It is in combination with other numbers that this sign manifests itself. But, as soon as you multiply or divide any of the numbers by zero, the number disappears, i.e. also becomes zero. In this case, this manifestation of zero is considered a divine aspect, and characterizes the sign 0 as the controlling force of the Absolute.

In natural manifestation zero symbolizes everything unmanifested, the union of the eternal flow of time and the infinity of space.

Zero in the human aspect symbolizes death, the transformation of life force into a different state. This death can be not only physical, but also spiritual, material.

Phrases like “Zero without a stick”, “You are a complete zero”, etc. are associated with a complete fiasco of the human condition.

Graphic representation of zero

• The ancient Mayans depicted it in the form of a shell.
• The Greeks did not have a zero in their number system, and the empty space was replaced by the letter "o", meaning "nothing".
• But the “conscious” designation as the number “0” in its current form was first discovered in Indian works only towards the end of the first millennium AD.

The symbolic image of zero is an egg, when the state of life already exists, but it has not yet manifested.

Zero or null (both forms are acceptable in speech and writing) divides the boundary between positive and negative and is considered a reference point. And where we go depends on ourselves.

I wish everyone to be cool as an egg, in the positive sense of this whole phrase, and to have many zeros after any perfect number. Let it be 100,000,000……. hours of joy, money in your wallet or friends. Who needs what...

Perfect numbers are considered to be all single-digit numbers from 1 to 9..

Write about interesting properties of numbers. Pictures are welcome!

I am posting interesting properties of the number sent by Leib Aleksandrovich Shteingarts.

1. A number behaves completely uniquely in ordinary arithmetic operations:

2. A number is the only number that cannot be divided by.

3. A number behaves very peculiarly when raised to a power:

4. The factorial of a number is also quite unusual:

5. A number is the only real number that is neither positive nor negative.

6. In the center of Budapest (Hungary) there is a monument to ZERO.

The number means the beginning of all roads in Hungary. All distances in the country are measured from this monument.
Zero is the only number that has a monument to it.

7. In set theory, Georg Cantor denoted the minimum cardinality of infinite sets (that is, the cardinality of countable sets) as follows:

8. Until the end of the 19th century, various countries used their own national ZERO meridians to measure geographic longitude. As geodesy developed, the lack of a standard system of longitudes was considered inconvenient by the international astronomical community.

In 1884, at the International Meridian Conference in Washington, it was proposed to take the Greenwich meridian as the origin of longitude (that is, the ZERO meridian) throughout the globe.

9. The number 0 has two names: ZERO and ZERO.

Both names in free use are equal. But in some common expressions these words are not interchangeable. For example, only zero in the expressions:

But only zero in such expressions:

10. Absolute ZERO temperature is the minimum temperature limit that a physical body can have in the Universe. Absolute zero serves as the origin of the absolute temperature scale. On the Celsius scale, absolute zero corresponds to a temperature of −273.15° C.

11. Of all the vectors, only the ZERO vector cannot be depicted as a directed segment.

12. On any calculator, after turning it on, a SINGLE number immediately appears - the number.

13. The first digit of a natural number can be anything except .

14. 4. At midnight, four ZEROS appear on the electronic clock.
A new day begins!

15. TIC TAC TOE is a logical game in which one of the players plays with “crosses” and the other with “toes”.

16. Only the number is written exactly the same as one of the letters - namely, like the letter O.

Previously, the number was written with a dash inside the sign (sometimes as the Greek letter Theta is written) to distinguish it from the letter O.

Zero without this stick was either a number or a letter. That’s why they sometimes began to say “ZERO WITHOUT A STICK”,

17. A hand gesture depicting the number in English-speaking countries means “EVERYTHING IS OKAY”, “EVERYTHING IS NORMAL”, “EVERYTHING IS EXCELLENT”.

18. The closed orbit of any cosmic body is an ELLIPSE, which in shape completely coincides with the shape of the number.

19. ZEROS of a function are numbers from the domain of the function at which it takes on a ZERO value.

20. The following property of number is very well illustrated by the famous poem by Samuil Yakovlevich Marshak.

21. On a computer keyboard, the numbers are shown in this order:

This number sequence is ALMOST increasing. The only thing that disturbs the order is the number.

22. In 1964, the wonderful book “THE ADVENTURES OF NULIK” was first published. This “fairy tale, but not a fairy tale”, which was invented by Emilia Alexandrova and Vladimir Levshin about numbers, their mysteries and oddities.

And then a musical performance was created based on this book, and even a record was released.

23. This poem about ZEROS was composed by Doctor of Physical and Mathematical Sciences Herzen Isaevich Kopylov (1925–1976), whose wonderful problem on a regular polygon is also available in the BEAUTY SALON
(see clause 10)

Comments: 20

1. 1 Alexey:

   I believe that in paragraph 16 the interpretation of the expression “zero without a stick” is erroneous. Let us remember A.S. Pushkin: “We honor everyone with zeros, and ourselves with ones!” By stick is meant “unit” with a corresponding change in the proposed interpretation in paragraph 16.

2. 3 Label:

   This is how mathematicians accepted it - by definition.
   For various reasons, mathematicians found it CONVENIENT.
   This cannot be proven.
   Just as, for example, it is accepted that
   .

   .
   .
   This is also accepted BY DEFINITION.

   Elena Reply:
   June 2nd, 2013 at 1:00

   Not at all.
   (a^n):(a^n)=1,
   On the other hand
   (a^n):(a^n)=a^(n-n)=a^0
   from here
   a^0=1

   Elena Reply:
   June 2nd, 2013 at 1:10

   About 0!
   1! = 1
   2! = 1!*2
   2! = 2
   3! = 2!*3
   3! = 6
   4! = 3!*4
   4! = 24
   and so on
   and now back
   4! = 24
   3! = 4!/4
   3! = 6
   2! = 3!/3
   2! = 2
   1! = 2!/2
   1! = 1
   0! = 1!/1
   0! = 1

   Or based on a combinatorial problem, where the factorial actually came from
   3 different objects can be placed in 3!=6 ways.
   2 different objects 2!=2 ways
   1 item – in one way (the item just exists) 1!=1
   0 items – again in one way (there are simply no items) 0! = 1

3. 4 Technik:

   5. The number 0 is the only real number that is neither positive nor negative...? Let's refute it... using an electric circuit.
   Hello!
   Open the textbook by Bessonov L.A. TOE (1978) chapter 8, §8.4 (§8.7) fig. 8.3.
   To represent the parametric state of an electrical circuit with a certain
   element (inductance for example) before and after switching, always zero
   accepts a sign character! t= 0- and t= 0+!!! It does not accept on its own,
   This is how mathematicians imagine it. Zero itself is zero

4. 5 Gennady:

   No number can be both positive and negative at the same time. Otherwise it won't be a number. Zero is, after all, a number, and is generally considered positive. Maybe because they put a minus sign in front of it only in special cases.

   Factorial 0! in itself does not make sense, based on the direct definition of factorial (I recently wrote about this). Mathematicians have agreed to consider 0!=1, since this helps to simplify and make many formulas more convenient and beautiful, for example, in discrete analysis.

   Two to the power of 0 is equal to 1, and this is proven in the theory of limits: the value approaches exactly 1 as it approaches infinity.

   Heart-shaped glasses Reply:
   June 15th, 2014 at 0:13

   Namsek Reply:
   May 26th, 2015 at 18:59

   Sorry for writing in English but I’m learning Russian and I don’t know grammar well enough yet.

   When I was 4 years old and I had just been told at school that there were odd and even numbers, I asked my father whether zero was odd or even. He replied “what the hell of a question is that?”
   Twenty years later I thought about it again and I concluded that it was neither, since it doesn’t exist. There I also understood that it IS NOT actually a number.
   Numbers are quantifications of something, zero is nothing. It means there is nothing to quantify.

   Zero is used in mathematics to mean an empty space. It means “nothing”. And nothing is no way on earth, positive, negative, odd or even.
   To be clear, there is nothing that could be negative or positive there. Nothing is there and nothing is missing.
   Positive numbers are energy/matter becoming stars, negative numbers are energy/matter becoming black holes. Zero is the void. The void cannot become a star or a black hole.

   The question does not subsist.

   Btw, zero “is” odd. It can’t be divided by two.

5. 6 Georgiy:

   Are you mistaken about Budapest?
   This is kilometer zero! The beginning of all roads in Hungary.
   It says KM at the bottom.
   In Moscow, too, there is a zero KM near Red Square, but it has zero relation to the ZERO monument.

6. 7 Gennady:

   I'll try to protect the number 0.
   The attitude of the respected author and many commentators towards zero (Hamcek was especially surprised and upset) inspired a well-known picture: ancient times, meadow, sheep grazing, night, a shepherd counting the stars - 1, 2, 3, etc. The shepherd associates stars and, probably, identifies them with numbers. There are stars - there are numbers. What if it’s cloudy and there are no stars? How many stars are zero in this case? What is this number zero? Since there are no stars, then there is no such number. Not a number, but an empty space, a vacuum. This is exactly what Hamcek writes - the void.

   But now we know that the number zero exists. They came up with the number 0 for him, and you can’t do without this number. Don't like the order of numbers on your computer keyboard: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0? Are the numbers not increasing? A zero at the end of the list spoils the whole picture, and does that mean the zero is somehow strange? No, there's nothing wrong with the zero, it's just that the numbers on the keyboard are placed incorrectly. Place zero at the beginning of the row if we want to rank the numbers. In this case, zero will rightfully take the leading place, zero heads the column of numbers, and it is from zero that the countdown of time at midnight begins. I am sure that zero will also lead the natural series of numbers. Not everyone agrees with this, but it is a matter of time.

   Let's take the ancient shepherd thousands of years into the future. Negative numbers have appeared, they are necessary, and everyone agrees with this, except our shepherd. He thinks in his own categories. Kolya has 3 apples, Vanya has 2 apples, but for some reason Masha has 5 apples. The shepherd will ask: “What happened? Has Masha already eaten her five apples or does she owe these apples to someone?

   If we add or subtract two numbers, the result is also a number, and that number may be zero. Zero - even number and is divisible by 2 without a remainder (http://ru.math.wikia.com/wiki/Even_and_odd_numbers).

   2 + (-2) = 0. What does this mean, what can it be compared with? I will use the allegories of the commentator Hamcek. Zero is neither matter nor antimatter, zero is the result of the annihilation of matter and antimatter, the result of the collision of a star and a black hole. Zero is an explosive number, it is the number of chaos, disorder, unbridled entropy. Therefore, zero is also a dangerous number. If zero is nothing, then this is a “nothing” that mathematicians will still struggle with in the 21st century.

   But you can divide by zero, why not? We get infinity, a transfinite number (http://ega-math.narod.ru/Singh/Cantor.htm). But we need to clarify, in accordance with the conditions of the problem or example, what kind of infinity we are dealing with. The minimum transfinite number is the cardinality of a countable set. Here we have to put up with, for example, the fact that the number of all natural numbers and the number of even numbers is the same. The next transfinite number is the power of the continuum. And here they will prove to us that there are as many points on the entire number line as there are on the interval (0,1).

   There is an infinite (apparently countable) set of transfinite numbers. And if we simply divide a certain number by zero, then uncertainty arises only in the sense that we need to decide on a transfinite number.

7. 8 Alexander Berezhnoy:

   Zero is also the only number about which mathematicians disagree. Should zero be considered a natural number or not? At school they don’t consider zero a natural number, but in vain...))

One of the most interesting numbers in numerology it is 0. She takes an active part in a person’s life. Zero is the beginning and end of everything, infinity. The ancient sages believed that it denotes divine power.

Feature 0 in numerology

The number 0 in numerology conceals sacred meaning about the spiritual beginning of his material nature. Zero is an anti-number and ranks first in the number series. It hides the great potential of the entire system of creations.

The English occultist and tarot reader A. Crowley described 0 with a mathematical numerological formula: 0=2, where 0 (Nuit or not I) means universal expansion and 2 (Hadit) - universal compression.

In numerology, the number 0 is the beginning of everything, the spiritual root cause of existence.

The sacred meaning of zero is explained by its shape. She is equated to the divine world. The round shape means infinity. It has neither beginning nor end.

Positive traits of number 0

Positive zero value:

• the beginning of everything;
• all-consuming energy;
• harmonious relationships;
• laws of the universe.

In numerological characteristics, the number means hidden possibilities and strengths that are inherent in a person from birth. To reveal them, you need to understand the signs of fate and do everything to achieve your goal.

The meaning of the number zero in the date of birth is reserve forces from past lives and reincarnations. Man knows nothing about their existence. For these qualities to change life, a person needs to make a choice between good and evil.

The repeated number 0 in the date of birth means poor development of the spiritual life of the individual. In numerology, this number is considered as a journey into your own spiritual world. If we neglect this possibility, the reserve power inherent in a person will turn into evil and bring harm not only to him, but also to his environment.

Negative traits of number 0

Negative qualities of zero:

• emptiness;
• death;
• secrets;
• lack of consciousness;
• chaos.

Human desires regulate the secret forces of zero. They create or destroy energy depending on the direction.

In numerology, death has a metaphysical meaning. Just like in Tarot cards, death signifies the completion of the life cycle. It requires renewal of consciousness, soul, body and new transformations.

Mysticism of number 0

The number 0 is the number of God and universal energy. It increases the strength of the numbers that are near it. Zero unites all values ​​and brings them to their logical end. This symbolizes God's power, which always comes back to its source.

Zero means freedom from prohibitions in the material world. This is the starting point of all energy and mysticism. A series of repetitions of this number makes it clear that it is worth thinking about your own spiritual world, its fullness and energy.

The frequent appearance of zero in a person’s life is a sign. Intuition will help you decipher it.

Numbers 1 and 0 in destiny numerology

Every person has masculine and feminine principles. They are represented by the numbers 0 and 1. The spiritual part of numerology considers human destiny through the prism of the interaction of the numbers 0 and 1. Such cooperation is usually denoted by the number 10. A person in numerology symbolizes a ten, but not always.

There are people who personify the number 2. It denotes the entire material part of people’s lives and activities. The more such values, the more twos. Ten characterizes the spiritual aspects of life.

Also in spiritual numerology there is a clear restriction on the use of tens. It is taken when it comes to a person’s energy and his plans. If you need to reveal the character or needs of an individual, it is better to use two.

Esoteric meaning 0

In esotericism, zero is nothing, but it does not mean emptiness. Nothing is the moment of maturation and accumulation of energy of other numbers.

Esotericism explains zero as the freezing of space and time. It stops any movement. He does this deliberately so that energy has time to accumulate and create a new impetus for life.

To understand the meaning and significance of the number 0, it is enough to imagine a few seconds before a strong explosion. Intense energy stands edgewise in the air, as if accumulating something. The silence hurts the ear, the emptiness evokes fear, but intuition tells us that something irreparable is about to happen.

Feminine essence 0

Zero is often compared to the feminine principle. A pregnant woman is the personification of this figure. The child is not visible, not heard, but he exists, accumulates energy, grows and prepares for birth.

The original meaning of the number 0 is to be born on the eve of anxiety and anticipation. This feeling is consuming. You can always guess, but your inner instinct will tell you the exact information.

Conclusion

The number zero in numerology and esotericism has a similar meaning. It cannot be calculated by date of birth. It will never be a personal characteristic number. This is a sacred number.

She is compared to deity and the feminine principle. Zero is an energy accumulator before the start of a big undertaking.

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.

No wonder the most terrible natural phenomena similar in shape 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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Character and inclinations were determined by numerical values, and the future was also predicted. Nowadays, the science of numbers has made great progress. And now numerology allows you to calculate even such an important event as the date of marriage.

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 can do 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 when different meanings angle 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 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 symbols 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 essentially everything was 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 logical paradox it can be 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.