15 mathematical Fact that perhaps you did not know about the number 0

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In 2005, Alex , a gray African parrot starred in current scientific news in the field of cognitive psychology when he proved to be able to understand a concept similar to that of no unit, that is, zero. What seems like an anecdote is actually very relevant, since understanding the concept of nothingness requires a level of reasoning that until now was only believed possible in humans (we learn it around 3 or 4 years) and in some primates . Alex, his brain the size of a hazelnut, came to give us a bath of humility

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Returning to zero and its understanding, it has not been easy for humans either to get the idea that to count and handle numbers with ease and ease, it is necessary to understand what is when there is nothing. Mathematical calculations, the laws of physics and computer programs need this idea to accurately reflect reality. The latter, for example, are based on the binary system of ones and zeros.

Nor has it been easy for humans to get the idea that to count and handle numbers, it is necessary to understand what is when there is nothing

Although we find zero in our day to day (take a ticket from your pocket, there you have one, or if you are lucky, many), there are many surprising curiosities about this number.

  1. Zero is a mathematical concept, but also a physical and philosophical one. It is a way of representing nothingness, emptiness, and it has interested and confused scientists and sages for much of history. What does an empty space mean? If it is empty, does it have any meaning? It is useful for something? Does it affect your surroundings?
  2. Although for us it is an almost instinctive concept associated with learning numbers when we are little, some of the ancient civilizations that we consider more advanced, such as the Egyptian, the Greek or the Roman, did not have an idea for zero, and had Logic that was so: why would they count nothingness as a number? If you have two apples, you see them and count them. If you owe someone an apple, you also know: you have less an apple. But zero apples is nothing, why would it be necessary to dial it with a number?

Zero has two functions: one is to represent nothing, and the other is to ‘save the place’ when there is nothing and give way to the next decimal3. But zero as we use it today fulfills two functions: one is to represent nothing, and the other is to save the place when there is nothing and give way to the next decimal place. For example, in the number 608, it serves to indicate that there are not tens without being confused with the number 68.

  1. This second function was present in cultures like the Sumerian. The Sumerian scribes chose to leave an empty space between some numbers to differentiate them (just as we use 0 to distinguish 68 from 608), but each left a different distance and what was a gap could be confused with two. When they realized it, they began to use a kind of apostrophe to indicate the absence of a number.

Statue of the Indian mathematician and astronomer Aryabhata
Statue of the Indian mathematician and astronomer Aryabhat

  1. It is not entirely clear when and where zero was invented. Most scholars point out that the Indian mathematician Aryabhata (mid-5th century) was the first to recognize and apply the concept of empty position in his number writing system, although he had no symbol to represent it. Also some pre-Columbian cultures, like the Mayans, used the idea of zero.
  2. Leonardo de Pisa, better known as Fibonacci, is famous, in addition to the succession that bears his name, for having introduced into Europe the Indo-Arabic number system that we use today, which uses the positional notation of base ten and zero. However, Fibonacci differentiated between zero, which he calls a brand, and the other figures (1, 2, 3, 4, 5, 6, 7, 8, 9), which he calls numbers.
  3. Neither in the Gregorian nor in the Julian calendar exists year zero: from December 31 of year 1 before Christ it is passed to January 1 of year 1 after Christ.
  4. In fact, this is so because the years, like the days or the centuries, are not counted with cardinal numbers, but are ordered with ordinal numbers, among which the number zero is not included (there is no zero position in front of the first position).
  5. Remember when we were hotly debating whether the 21st century started on January 1, 2000 or 2001? Since there was no year zero, the one who celebrated it in 2000 was actually celebrating the passage of 1999 years. We are sorry we are so late in solving the dilemma.

The years are not counted with cardinal numbers, but are ordered with ordinal numbers, among which the number zero is not included10. So when did the concept of the year, hour or zero minute come up? Well, it is relatively recent, from the second half of the 20th silo. It was born from the g

11. Zero is a number with some unique properties: it is the only real number that is neither positive nor negative, nor is it even or odd.

12. In mathematics, zero is sometimes called additive identity because adding it to any number does not change its value: x + 0 = x.

13. It also has unique characteristics applied to other mathematical operations: any number multiplied by 0 equals 0 and any number raised to 0 equals 1.

14. Divisions by zero are also a question that mathematicians have turned around a lot. This operation, from the point of view of algebra and arithmetic, is considered an indefiniteness, that is, when dividing any number by zero, we do not obtain a defined value. This is so for the following reason: if we seek to calculate 12/0 = x, that means that 0 multiplied by x would have to be = 12. But there is no number that multiplied by 0 gives 12 as a result (remember: any number multiplied times 0 equals 0). So it is often said that any number divided by 0 results in infinity. 

15. There is the concept of absolute zero, although it corresponds to the branch of physics and not mathematics. This is the name given to the lowest temperature that can theoretically be reached, in which the energy level of a system is so low that there is no movement. Absolute zero corresponds to zero on the Kelvin temperature scale, so it corresponds approximately to negative 273.15 degrees Celsius. 

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