The numbers are an absolute phenomenon of human civilization and
culture. They are a human invention. The numbers are all around us. They
are the few things that each of us remember from school maths lessons.
We use the symbols for numbers in all spheres of our lives, not just
professional but also personal. Surely, there is no one who does not
know the numbers. What does life would be without these symbols? If
suddenly in a strange way, these signs disappear and people lose their
memory for them, I think surely humans would take the same path all over
again - using lines and combinations of traits to show an increased
quantity. People have come a very long way to discover the idea that
things in the real world around them change and grow in quantity.
However, not only in quantity, but also as a sequence. Moreover, people
have invented way to indicate the situation when we suffer loss or
something reduces its quantity. The numbers are qualified also as
positive and negative.
When and where, for what purpose we use numbers? The answer to this question will help us to get back to the main purpose of our lessons - the value of mathematics in our real life of non-mathematicians. Let us do a simple calculation - how many times in a day we have to use a number as a symbol or as a word? If our profession is such that the numbers are part of our professional language, that means we are talking in the language of the numbers the whole day. The accountants, the economists, the tax inspectors, the teachers in mathematics, the computer programmers and much more professions - all supposedly expresses themselves best in the language of numbers. From their combinations, they are able to send messages and to tell stories that will reach their audience decoded and understood adequately. People from other professions mention also the numbers many times in a day. When getting up in the morning we see the numbers on our alarm clock. The numbers accompany us throughout the day. When we use our watch, we see numbers. When we need to go to the shop to buy something, we see the numbers as prices on products. When someone wants some specific information from us, related to our age, weight, height, year of birth, how many years we live in a certain place and so on, we use numbers to answer. In all these real life situations, we use numbers. When we cook in the kitchen, we constantly measure our products and we express the weight in numbers. In these cases, we use numbers as a symbol or word. The figures are part of our memory of our lives, which can be represented in this way. When we ask ourselves how long, we have not seen a certain person, we think about numbers as well. The numbers are part of the vocabulary of any natural language - they are presented in idioms, proverbs and sayings. If we try deliberately to list how many times in a day we mention the numbers without even being mathematicians we will probably struggle to answer specifically because consciously or not the numbers are part of our idea and vision of the world. Our human brain is designed in a way that sees the real objects around us as single and multiplied by themselves several times, and also as different, but more than one. The same is true for the abstract concepts that although we cannot see and touch, we can imagine as single or multiplied. Everybody had at least one love in his or her life. However, some had and many more loves, joys, pains, sufferings, hopes. Nevertheless, we all have one life of our physical body, as far as we know.
With the recognition of the numbers links the idea to count. Counting in itself means that we see objects in gradation in their growth as quantity. How many numbers do we have when we are counting? We operate with ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. From their combination, we can create infinitely large numbers. Let us not forget that we already introduced the concept of the "mathematical infinity", which we have when to any combination of numbers, we can add new and new numbers and practically it may never ends. In fact, here we discuss only integers, with the others we will deal separately. What is an integer, or a whole number? It is usually associated with the idea of full, undivided subject or object, quality, process.
An interesting phenomenon is the idea of a sequence, and that is something we also use constantly in our real life. It is about counting, but mostly is used for comparing things. We compare constantly – very often we want to know which one is first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth and so on.
Furthermore, we constantly arrange the numbers in a sequence, resulting from their internal numerical hierarchy. We daily perform similar operations, such as knowing where to put the number 4 before 5 or after 5. When we are in a queue in a shop, for example, we automatically count people in the queue to find out when it will be our turn. Here it helps us the ability to count, compare and arrange, but not so much the numbers as real objects that the numbers represent. When we are in a shop, we automatically compare the prices and we decide do we have that much money available.
Yes, the numbers exist to indicate something real. What exactly do the numbers mean a symbol of what they are? We cannot give a definite answer to this question - they may be a symbol of everything and symbol of nothing simultaneously. When we use the symbols of the numbers, then they are absolutely specific and precise. For this reason, there is a general impression of mathematics that it is an exact science. Because when we see the numerical symbols 2 or 4, we imagine exactly 2 or 4 numbers of things. What kind of things? Here the mathematics from exact science becomes abstract because the power of numerical symbol is that they may have a different volume. For example, when we say "two apples" and "two galaxies," are they equal as a quantity? As a quantity, yes, they are equal, but the volume of number 2 will be completely different because it is clear that the apple is something small, while the galaxy is difficult to measure. The power and the magic of the numerical symbols is that behind them can stand everything from the visible and invisible world.
What we imagine when we see the numerical symbol 0? Isn’t it brilliant to have a symbol for “nothing”? Because exactly that is what the zero means – an absence or a lack of presence of something. Zero is truly brilliant symbol to indicate nothing. It is in this sense we constantly use the sigh of zero - from the absence of something, to more abstract use, such as "I have zero respect for you”. However, the zero is really a magical sign, because it has the incredible ability to make a huge magic, such that for a second to turn you into a billionaire. Let us try to write any number on a piece of paper, and now put behind the number as many zero, as you want. In this case, the zero has the power to make you rich with the power of mathematical infinity, which means infinite richness.
The numbers besides all this have the glory to be positive and negative. It does not sound like a very good fame, if you do associations with the positive and negative qualities of people, for example. However, with the numbers is a little bit different. Which number is a "positive" number? Any number that means that we have something or a process is going. For example, the number of our age is a positive number because we are alive. Which number is a "negative" number? Simply put each number before which we write a minus sign and which is used to indicate that something decreases in quantity or quality. Any number that is less than zero, is a negative number. So it turns out that zero is not the smallest number, although it is able to indicate “nothing”? That means that zero has many uses: it may mean nothing, but it may increase the value of numbers, placed after them. There are numbers less than zero, such as -1, -2, -10, etc. . . . For example, 5 and -5, the first is a positive number and the second is a negative number. The negative numbers are used for example to show freezing temperatures on the thermometer, the temperatures below zero. Depending on whether it is 20 degrees out or -20 degrees, means that at least our clothing out will be different because in the first case it will be hot, and in the second - an incredibly cold. When it comes to a bank account, then negative numbers would mean that our account decreases, and we have less money. When we are working with negative profit, so in fact that means that we have a loss but not a profit.
Many researcher have noted that people are born with a "number sense" with a genetic ability to notice how things change in numbers. In addition, many believe that many animals and birds are able to distinguish one egg and more eggs for example.
One task for you: Take a piece of paper and a pencil and start recording any case, when you need to use symbols for numbers – from the morning till the evening. I guess your list will be long, because the numbers are part of our vision of the world.
What we learned in this lesson:
- When we are using symbols for numbers.
- Counting and sorting numbers.
- Number and ordinal numbers.
- Symbol for zero 0.
- Positive and negative numbers.
In our next lesson about the numbers, we will learn how to compare them, about their history; different types of numbers that existed in different cultures around the world; the sacred and divine meaning of some numbers; the number "pi" and the names of the numbers in different languages.
(Elena S. Lyubenova)
When and where, for what purpose we use numbers? The answer to this question will help us to get back to the main purpose of our lessons - the value of mathematics in our real life of non-mathematicians. Let us do a simple calculation - how many times in a day we have to use a number as a symbol or as a word? If our profession is such that the numbers are part of our professional language, that means we are talking in the language of the numbers the whole day. The accountants, the economists, the tax inspectors, the teachers in mathematics, the computer programmers and much more professions - all supposedly expresses themselves best in the language of numbers. From their combinations, they are able to send messages and to tell stories that will reach their audience decoded and understood adequately. People from other professions mention also the numbers many times in a day. When getting up in the morning we see the numbers on our alarm clock. The numbers accompany us throughout the day. When we use our watch, we see numbers. When we need to go to the shop to buy something, we see the numbers as prices on products. When someone wants some specific information from us, related to our age, weight, height, year of birth, how many years we live in a certain place and so on, we use numbers to answer. In all these real life situations, we use numbers. When we cook in the kitchen, we constantly measure our products and we express the weight in numbers. In these cases, we use numbers as a symbol or word. The figures are part of our memory of our lives, which can be represented in this way. When we ask ourselves how long, we have not seen a certain person, we think about numbers as well. The numbers are part of the vocabulary of any natural language - they are presented in idioms, proverbs and sayings. If we try deliberately to list how many times in a day we mention the numbers without even being mathematicians we will probably struggle to answer specifically because consciously or not the numbers are part of our idea and vision of the world. Our human brain is designed in a way that sees the real objects around us as single and multiplied by themselves several times, and also as different, but more than one. The same is true for the abstract concepts that although we cannot see and touch, we can imagine as single or multiplied. Everybody had at least one love in his or her life. However, some had and many more loves, joys, pains, sufferings, hopes. Nevertheless, we all have one life of our physical body, as far as we know.
With the recognition of the numbers links the idea to count. Counting in itself means that we see objects in gradation in their growth as quantity. How many numbers do we have when we are counting? We operate with ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. From their combination, we can create infinitely large numbers. Let us not forget that we already introduced the concept of the "mathematical infinity", which we have when to any combination of numbers, we can add new and new numbers and practically it may never ends. In fact, here we discuss only integers, with the others we will deal separately. What is an integer, or a whole number? It is usually associated with the idea of full, undivided subject or object, quality, process.
An interesting phenomenon is the idea of a sequence, and that is something we also use constantly in our real life. It is about counting, but mostly is used for comparing things. We compare constantly – very often we want to know which one is first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth and so on.
Furthermore, we constantly arrange the numbers in a sequence, resulting from their internal numerical hierarchy. We daily perform similar operations, such as knowing where to put the number 4 before 5 or after 5. When we are in a queue in a shop, for example, we automatically count people in the queue to find out when it will be our turn. Here it helps us the ability to count, compare and arrange, but not so much the numbers as real objects that the numbers represent. When we are in a shop, we automatically compare the prices and we decide do we have that much money available.
Yes, the numbers exist to indicate something real. What exactly do the numbers mean a symbol of what they are? We cannot give a definite answer to this question - they may be a symbol of everything and symbol of nothing simultaneously. When we use the symbols of the numbers, then they are absolutely specific and precise. For this reason, there is a general impression of mathematics that it is an exact science. Because when we see the numerical symbols 2 or 4, we imagine exactly 2 or 4 numbers of things. What kind of things? Here the mathematics from exact science becomes abstract because the power of numerical symbol is that they may have a different volume. For example, when we say "two apples" and "two galaxies," are they equal as a quantity? As a quantity, yes, they are equal, but the volume of number 2 will be completely different because it is clear that the apple is something small, while the galaxy is difficult to measure. The power and the magic of the numerical symbols is that behind them can stand everything from the visible and invisible world.
What we imagine when we see the numerical symbol 0? Isn’t it brilliant to have a symbol for “nothing”? Because exactly that is what the zero means – an absence or a lack of presence of something. Zero is truly brilliant symbol to indicate nothing. It is in this sense we constantly use the sigh of zero - from the absence of something, to more abstract use, such as "I have zero respect for you”. However, the zero is really a magical sign, because it has the incredible ability to make a huge magic, such that for a second to turn you into a billionaire. Let us try to write any number on a piece of paper, and now put behind the number as many zero, as you want. In this case, the zero has the power to make you rich with the power of mathematical infinity, which means infinite richness.
The numbers besides all this have the glory to be positive and negative. It does not sound like a very good fame, if you do associations with the positive and negative qualities of people, for example. However, with the numbers is a little bit different. Which number is a "positive" number? Any number that means that we have something or a process is going. For example, the number of our age is a positive number because we are alive. Which number is a "negative" number? Simply put each number before which we write a minus sign and which is used to indicate that something decreases in quantity or quality. Any number that is less than zero, is a negative number. So it turns out that zero is not the smallest number, although it is able to indicate “nothing”? That means that zero has many uses: it may mean nothing, but it may increase the value of numbers, placed after them. There are numbers less than zero, such as -1, -2, -10, etc. . . . For example, 5 and -5, the first is a positive number and the second is a negative number. The negative numbers are used for example to show freezing temperatures on the thermometer, the temperatures below zero. Depending on whether it is 20 degrees out or -20 degrees, means that at least our clothing out will be different because in the first case it will be hot, and in the second - an incredibly cold. When it comes to a bank account, then negative numbers would mean that our account decreases, and we have less money. When we are working with negative profit, so in fact that means that we have a loss but not a profit.
Many researcher have noted that people are born with a "number sense" with a genetic ability to notice how things change in numbers. In addition, many believe that many animals and birds are able to distinguish one egg and more eggs for example.
One task for you: Take a piece of paper and a pencil and start recording any case, when you need to use symbols for numbers – from the morning till the evening. I guess your list will be long, because the numbers are part of our vision of the world.
What we learned in this lesson:
- When we are using symbols for numbers.
- Counting and sorting numbers.
- Number and ordinal numbers.
- Symbol for zero 0.
- Positive and negative numbers.
In our next lesson about the numbers, we will learn how to compare them, about their history; different types of numbers that existed in different cultures around the world; the sacred and divine meaning of some numbers; the number "pi" and the names of the numbers in different languages.
(Elena S. Lyubenova)
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