I am a zero in mental arithmetic. It’s true, I fight with this ability, but I want to concentrate on the phrase it is. In our language, we or we equate zero with something negative. But zero is the only real number that is positive or negative. It is neutral.
Why the negative association? Humanity has housed strong feelings towards zero; It was prohibited in some places in a moment. Xenophobia and hero ideology supports this powerful concept. However, today all mathematics are based on this number.
Define “zilch”, “nil” or “0” is not easy. In fact, neuroscientifics have studied how we live in any varied ways. It should not surprise, then, that cultures have been approached zero in different ways of time.
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But the surprising thing is how long people arrived without this concept. The numbers have accompanied humanity throughout history. The oldest documents record them. Trade cannot be done without them, and are necessary to measure the earth or register a recipe for beer. Zero is something unusual and is not strictly necessary for all these activities.
As a result, it was several millennia for zero to be accepted as a number in its own right. People have resisted repeatedly. However, today we know that all other numbers, and all modern mathematics would really be nothing without zero.
A story of absence
Zero may have been invented more than once, with different functions. For example, about 5,000 years ago the Babylonians had a concept of zero, but it was a number that defended itself. Instead, an American use value system is used to indicate numbers: if I write three digits in a row, such as 145, then the first number corresponds to the place of Huleds, the second to the tens and the last one to which (or units).
The Babylonians used a similar Apple system was not based on 10 but on 60. In a place value system, it needs a zero to distinguish a number like 105 of 15. Babylonians use that inserting a space, Whatich is a space, it is a space, a space, a space, a space of space, a space of space, a space, a space, zero, zero.
It is also notable that many ancient societies have presented without this concept. In ancient Greece, all kinds of advanced mathematical considerations were made (I only think of the Pythagoras theorem or the basic pillars of logic by Aristotle) without a zero per se. The abstract concept of nothing was well known by the ancient Greeks, but they considered it part of logic, not mathematics. Zero is strange, after all. For example, no number can be divided by zero. The ancient Greeks did not like this property.
The exact origin of zero as we use today has the issue of some debate, but we know that in the seventh century AD.
Previously, mathematical problems are generally illustrated using geometric objects. For example, you may want to know how two rectangular fields can be connected to form a piece of square or equal size. Negative numbers are irrelevant to such tasks, as is zero.
However, Brahmagupta was also interested in such abstract problems. To use these new numbers correctly, I first needed a functional set of rules that clearly specific about how to deal with the thesis amounts. In his book Br & Amacr; HMASPHUṭASIDDHANT & AMACR;For example, he wrote that the sum of two positives is positive, the sum of two negative negatives, and the sum of a positive and a negative is its difference; If they are the same, it is zero. Hey, also, that the sum of a negative and zero is negative, that of a positive and zero is positive, and the sum of two zeros is zero.
In a similar style, Brahmagupta also described how to multiply and divide the new numbers. The rules established by about 1,400 years are the same as we learn in school today, except one. The zero defined by zero as zero, which is wrong from the current mathematical perspectives.
Zero gradually extends
Brahmagupta’s rules, together with the Indian decimal numbers system, extended rapidly through the world. The Arab scholars took the concepts and developed the system of Arab numbers, on which our modern numbers are based. From there, the zero and Arab numbers arrived in Europe, although at the time possible of sausages. The Crusades took place between the XI and XIII centuries, and with them came an immense rejection of all the ideas and knowledge of Arab or Islamic origin.
In Florence, Italy, this development culminated with the prohibition of zero number in 1299. At that time, the economy in that city was blooming, and merchants around the world joined together to sell their goods. In a city famous for banking and trade, zero raised a real problem: it was very easy to increase the size of a number in a piece of paper simply adding some zeros. A 10 quickly became 100 or even 1,000, while the Roman numbers system did not allow such manipulation. Therefore, city leaders decided to banish zero and trust the proven and tested Roman numbers.
But the calculation with Roman numbers is incredible complicated and cumbersome. Gradually, approximately more than 100 years, Arab numbers prevailed, including zero. In the fifteenth century, the concepts were finally accepted by society in general.
Much ado about nothing
At the beginning of the 20th century, the mathematician Ernst Zermelo created the set of rules on which modern mathematics is based. At that time, logic sought the simplest rules possible from which everything in mathematics could be stunned. Either numbers, systems of equations, derivations or geometric objects, everything must arise from some basic assumptions.
Zermelo developed nine simple axioms, that is, not proven basic assumptions, on which everything is based on mathematics. These are still used today. One of the axioms is: “There is an empty set.” This is something like the zero of the theory of the whole. That’s where everything begins, it’s “there is light!” Or mathematics. And, in fact, this is the only set that Zermelo built so explicitly. The other rules say, for example, that it can “combine two sets to form a third set” or “select an element of a set.”
Everything else follows from the empty set, the “zero”. For example, the numbers are built from it. To do this, it is useful to imagine a set as a bag in which you can pack objects. An empty set corresponds to an empty bag.
When building the numbers, Zermelo started with zero. It corresponds to the empty set or an empty bag. “One” is the amount in which the zero is previously defined, so it is an empty bag inside. Two is the amount contained in 1 and 0, or a bag that contains a bag that contains a bag. The 3 is then the amount contained in 2, 1 and 0 -Okay, I admit that it becomes confused.
Graphically, this can be represented a little better by ∅ Symbolizes the empty set:
0 = ∅
1 = {0} = {∅}
2 = {0, 1} = {∅, {∅}}}
3 = {0, 1, 2} = {∅, {∅}, {∅, {∅}}}}
Zermelo has put the foundations for integers. From here, all other numbers can be defined, including the negative number, fractions, irrational number, etc.
Mathematical concepts other than numbers can also be obtained in this way. You can gradually advance in complexity until it ends with the most abstract structures of modern mathematics. It is a luck for humanity that anyone comes to realize the power of zero as a starting point and accept it.
This article originally appeared in Der Wissenschaft spectrum And was reproduced with permission.
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