Numbers or the second step after the first word
Once we are a couple of months old, efforts to learn the first words follow right after the parents’ joy of the first steps. And from the first words such as a mom or dad slowly becomes one cube, two cars, or two red cars. More words we manage, we deal with numbers as a tool how to express quantity or order more intense. After some time, we learn the basic operations with numbers and over the time we use them as normal words with a value. Then, there comes time when we want to find out what numbers mean, what their subjects are and how we can express them. Original finger language was gradually replaced with "scrapes" to the plates, which were consequently transferred into complete sets of fonts.
Everything what is now controlled by modern telecommunication technologies and computer equipment is based on the principle of binary system. We listen to and rely on the simplest two symbols - one and zero. They were for sure described as numbers sometimes around 6th century AD. It is interesting, which numbers are considered as important and which numbers as irrelevant.
Number - its importance
Number is an abstract object used to describe an amount and order. The first numbers were probably contratallias that occurred in the third millennium BC. There were used jettons with notches which functioned for the exchange and expression of quantity in the Sumerian empire. Although these numbers were very transparent, the problem was that it was not possible to perform more difficult arithmetic operations with them. For this reason, it became a necessity to create numerical systems which give numbers an order and a strict hierarchy. With little exaggeration, we can say that numerical systems are nations that have their leader in front and the smallest number at the end. This model slightly suggests a society in which the system originated. Those rich, powerful and smart led the company - either in a fact or in a theory, while others less gifted created them ideal conditions for the creation of an ideal space of scope.
The Arabic numbers
The numbers, which originally evolved from the Brahmi numeral language. They have not got their origin in Arab countries, as it might seem, but in India. The reason, why they are called Arabic numerals is that the Arabs took them from North Africa to Europe thanks to the international trade and colonization, where they got their name and were disseminated further. They became the basis of the most widely used ie decimal system. It became popular all around the world
The Roman numbers
Roman numbers are numbers that use letters of the alphabet for their writing. Higher numbers used to be recorded by linking and repeating basic numbers. Number 999 was recorded as CMXCIX or IM. The Romans first did not use the numeral million, therefore, they did not have any designation for it. Capital letters were used for writing them. Using Roman numerals has still been retained for designation of chapters, pages, prefaces, months in calendars, time on watches, dates on the covers of magazines.
The Greek numbers
The Greek numbers are similar to the Roman numbers; however, every one, ten and hundred has its own symbol. The usage of this system today is virtually identical with the Roman numeral system. However, there is undoubted difference. Based on historical activities of individual empires ie. Roman expansion, acquisition of territory and frequent fights have led to the influence of wide area – by this ways it has gained stronger position towards less invasive method of existence of its empire in the late seventh century standing in decline and oppression of Islamic tribes.
Knowledge of numbers according to their types will allow us to look at the clock and know what the time is. Take a magazine that has its year of issue written on the front page and know from what date it is. See Roman inscription on a house and know when it was built. Full of this information, we begin to covet how to use numbers. This raises the question of how and where to go? The answer of numerical system is obvious. With its knowledge we gain the possibility of application numbers into complex formations, so called systems.
The Non-positional number systems
Value of a number is not given by the position in the sequence of numbers in this notation. Due to a frequent absence of zero, the notation of a very long and complex numbers and not using negative values, these systems are not suitable for today’s use. In the simplest non-positional numeral systems, the principle is in the addition of values of individual numbers or letters. However, the advantage is the addition and subtraction, which can be applied a little faster than the positional numerical systems.
The non-positional number systems function today rather for marking the chapters, pages, prefaces, months in a calendar, time on watch, or dates on the cover of magazines. Now we know that numbers can be in the systems that are governed by the rule of a position, and on this basis assigned characteristics or only experienced sequence that does not give more importance to individual numbers in the string. Can we be satisfied? Someone would say "yes." But I say, "NO!" After all, we encounter a problem, that is: what numbers and when to use them, as we can hardly buy minus one roll, do the square root of minus ten and look for logarithm of minus ten. The basic mathematics sometimes ends in this respect and in complementarity with understanding the depth of this problem, a new dimension of numbers develops.
are positive integers that are marked with capital letters N. This set is infinitely long. Furthermore, this category is divided into subcategories which are N +, which are positive natural numbers, N0 which are positive natural numbers including zero. With those we encounter every day. I take a shirt, two shoes, two pairs of socks when it's minus thirty and I'm happy. But, what if my salary does not cover the costs? I'm still in the field of natural numbers? For this purpose, I extended the numeric fields of integers.
consist of natural numbers, zero and negative numbers. They are denoted by a capital letter Z. They create an infinite countable set. The result of addition and multiplication of numbers from the field Z, we get an integer again, ie. it is closed on these operations. Associativity, commutativity, existence of neutral element and distributivity apply here for multiplication and division. Integers can express how broke a person, firm or state is, how much goods were exported and what amount was not. But imagine the example: there are five shipments. Out of the first shipment was exported only a half, out of the second shipment was also exported only a half, out of a third shipment was not exported one third, out of the fourth was not exported one quarter and out of the fifth shipment was not exported one fifth. Where will we find the answer? Let's try rational numbers.
The rational numbers
stand for real numbers, which can be expressed by an integer or a fraction - the ratio of two integers with different denominator from zero. It is marked by the capital letter Q. The fractions were used in about one thousand BC by Egyptians. Now, thanks to the ancient Egyptians we know that the total number of consignments intended for export were not exported one hundred and seven sixtieth. To solve this problem, we arrange a larger truck which goes to other places without additional cargo. But we need to find out how many tires will fit into the cargo space. Then, we must calculate the space that each tire needs to fit in. Now, because we want to fill the space with small additions, we calculate the content of tires. But the question is how?
are any real numbers that are not rational numbers. Therefore, it is a number that can not be expressed as a fraction. The set of irrational numbers is innumerable. These include some roots, logarithms, Euler number e and π. Around the year five hundred BC the Greek mathematicians began intensely be conscious of the need for irrational numbers. With the birth of irrational numbers, we can express quite challenging and difficult questions of science.
These are numbers, which we can assign points of the infinite line. They describe a specific distance from the selected point on a line. Then, zero divides these numbers into positive and negative. This field of numbers is amrked with R. Fractions were used in about one thousand BC by Egyptians. The set of real numbers is innumerable, thus, there are much more real numbers than natural numbers. You can further extend to the complex numbers - which contain solutions to all polynomial equations.
They are formed by extending the field of real numbers so that every algebraic equation has a solution. It can be denoted by the letter C. This number has two components. The first one is the real part (a) and the other is imaginary part (bi). They are mostly written in the form a + bi. The imaginary unit is defined as i2 = -1
They are extremely important especially in electronics, optics, hydrodynamics, physics and mathematics.
Now we have shown how important are numbers, but equally important is the interpretation of individual numbers and their meaning. Numbers may have slightly philosophical significance, which may not be ignored. So, when the words become numbers, we begin to look differently at the world around them. The fact that we are encouraged to analyze our lives more often, we sometimes forget that numbers can serve us for the fulfillment of amazing goals, but we must remember that a negative number does not belong to a healthy economy, that one is sometimes more than a million and that even one good deed can compete with a dozen of bad ones. Let the axiom of good people who will be the same for all as one and one is two - at "our level".