We regard everyone as zeros and ones of ourselves. But there is no friendship between us.

Whoever praises himself best of all ... He will become the most successful, beloved, happy person in the world. Everyone knows the saying: if you don’t praise yourself, no one will praise you. But alas, as practice shows, we do not know how to praise ourselves - we are even embarrassed. Then about what respect for yourself,

Write about interesting properties of number. Pictures are welcome!

I post interesting properties of the number that Leib Aleksandrovich Steingarts sent.

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

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 the city 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 digit to which a monument has been erected.

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 longitudes. As geodesy developed, the lack of a standard system of longitudes was found to be 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 longitudes (that is, beyond 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 set expressions, these words are not interchangeable. For example, only zero in expressions:

But only zero in such expressions:

10. Absolute ZERO temperature is the minimum temperature limit that a physical body in the Universe can have. Absolute zero serves as the starting point for the absolute temperature scale. On the Celsius scale, absolute zero is -273.15°C.

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

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

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

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

15. tic-tac-toe is a logic game in which one of the players plays with tic-tac-toe and the other player plays with tic-tac-toe.

16. Only the number is written in exactly the same way as one of the letters - namely, as 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 wand was either a number or a letter. Therefore, they sometimes began to say “ZERO WITHOUT A STICK”,

17. A hand gesture representing the number , in English-speaking countries, has the meaning “ALL IS OK”, “ALL IS NORMAL”, “ALL IS EXCELLENT”.

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

19. The ZEROs of a function are the numbers from the function's definition area, at which it takes the ZERO value.

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

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

This number sequence is ALMOST increasing. Only the number breaks the order.

22. In 1964, the wonderful book "ADVENTURES OF ZERO" was first printed. This “fairy tale but not a fairy tale”, which was invented by Emilia Aleksandrova and Vladimir Levshin, is 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 regular polygon problem is also available in the BEAUTY SALON
(see item 10)

Comments: 20

1. 1 Alexey:

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

2. 3 Leib:

   So mathematicians accepted - by definition.
   For a variety of reasons, mathematicians have found this to be CONVENIENT.
   You can't prove it.
   Just as, for example, it is accepted that
   .

   .
   .
   This is also accepted BY DEFINITION.

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

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

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

   Pro 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 the combinatorial problem, where did the factorial actually come from
   3 different items can be placed in 3!=6 ways.
   2 different items 2!=2 ways
   1 item - one way (just eat the item) 1!=1
   0 items - again one way (just no items) 0! = 1

3. 4 technicians:

   5. The number 0 is the only real number that is neither positive nor negative...? Let's refute ... with the help of a circuit, an electric one.
   Hello!
   We open the textbook Bessonov L.A. TOE(1978) ch.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 switching and after, necessarily zero
   accepts a sign character! t=0- and t=0+!!! Accepts not by itself
   so it is represented by mathematicians. 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 it is customary to consider it positive. Maybe because only in special cases they put a minus sign in front of it.

   Factorial 0! by itself does not make sense, based on the direct definition of factorial (recently wrote about it). 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 proved in the theory of limits: the value approaches precisely 1 as it approaches infinity.

   heart shaped glasses
   June 15th, 2014 at 0:13 am

   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 answered “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 George:

   Are you wrong about Budapest?
   This OK zero kilometer! The beginning of all roads in Hungary.
   It says KM at the bottom.
   In Moscow, there is also 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 to zero (Hamcek was especially surprised and upset) inspired a well-known picture: ancient times, a meadow, sheep graze, night, a shepherd counts 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 in this case - zero? 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 is. For him, they came up with the number 0, and you can’t do without this number. Do not like the order of numbers on the computer keyboard 1, 2, 3, 4, 5, 6, 7, 8, 9, 0? Are the numbers going up? The zero at the end of the list spoils the whole picture, so the zero is somehow strange? No, everything is fine with zero, it's just that the numbers are incorrectly placed on the keyboard. 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 leads the column of numbers, it is from zero that the countdown begins at midnight. I am sure that zero will also lead the natural series of numbers. Not everyone agrees with this, but it's a matter of time.

   Let's move the ancient shepherd millennia forward. Negative numbers have appeared, they are necessary, and everyone agrees with this, except for our shepherd. He thinks in his own terms. 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 those apples to someone?

   If we add or subtract two numbers, then the result is also a number, and that number may be zero. Zero is an 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 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 it is such a “nothing” with which mathematicians are still tormented in the 21st century.

   And you can divide by zero, why not? Let's get infinity, a transfinite number (http://ega-math.narod.ru/Singh/Cantor.htm). But it is necessary 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 one has to put up with, for example, the fact that the number of all natural numbers and the number of even numbers are 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 numerical axis as on the interval (0,1).

   There is an infinite (probably countable) set of transfinite numbers. And if we simply divide some 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 on which mathematicians disagree. Whether to count zero as a natural number or not. At school, zero is not considered a natural number, but in vain ...))