MATHEMATICAL SYMBOLS

Symbols are the basis of every culture. They are the main signs of human civilisations that carry through centuries people’s intelligence and observations of life. Through symbols people  can  express specific ideologies and social structures.  They are great metaphors of people’s abilities to create an abstract metalanguage which serves as a mediator between the knowledge and people. 

A symbol is a mark, sign, object action, sounds, colours, or word that stands for some ideas and beliefs  and relationships between them. Symbols allow people to go beyond what is known or seen by creating links between otherwise very different concepts and experiences. Symbolism is when something represents abstract ideas or concepts. Some symbols are gained from experience, while others are gained from culture. Language is the most often used form of symbolism. For example, the letters of an alphabet symbolize the sounds of a specific spoken language. Language is an important source of continuity and identity in a culture.

All communication is achieved through the use of symbols. The world is filled with symbols.  For example, a red octagon may be a symbol for "STOP". On a map, a blue line might represent a river. Numerals are symbols for numbers. Alphabetic letters may be symbols for sounds. Personal names are symbols representing individuals. A red rose may symbolize love and compassion. The variable 'x', in a mathematical equation, may symbolize the position of a particle in space. Sports uniforms, company logos, and traffic signs are symbols. In some cultures, a gold ring is a symbol of marriage. Some symbols are highly functional; stop signs, for instance, provide useful instruction. Gestures also have symbolic meaning. In cartography the symbols form a legend for a map.

The academic study of symbols and signs is called semiotics. Semiotics is linked with both linguistics and psychology. Semioticians thus not only study what a symbol implies but also how it got its meaning and how it functions to make meaning in society. Symbols are a tool of complex communication that often can have multiple levels of meaning. Language is a symbolic system through which people communicate and through which culture is preserved. Mathematics is a symbolic system too. 

How do we know that one symbol relates to mathematics, but not music, and even not to French language? The question may seem strange to someone, because our general cultural knowledge allows us to decide immediately what to which sphere of knowledge belongs. Every different field of human knowledge has their own expressive language and system of symbols.

For example, to become a good artist, you have to have a talent, of course, but before you know if you have a talent, you have to do something else. You need to learn how to draw with a pencil. Moreover, when you become bolder and you begin to like this activity, you can start using colours. In the beginning, you have to introduce to yourself the expressive language of symbols  in which artists communicate between themselves. You have to do that if you have decided that being an artist will help you to express better your own emotions, feelings, thoughts and attitude towards your inner world, and the world around.

It is the same with the music - maybe you can sing without knowing musical notes and this is commendable; your family will be very proud of you if you prove that you sing well. However, if you want to play some musical instrument and if you want to become a professional musician, you must learn the language and the symbols through which technically musicians record their music. Exactly, it comes through the musical notes. The process is the same with the French language - to learn to read and write in French, you have to learn French letters, to learn how to combine them with one another, the basic rules of grammar, and many other things but without knowing the letters you cannot read at all.

Mathematics is no different. It also has its own language and system of symbols by which exists and by which is recognized among the other areas of human knowledge. The language of mathematics is a symbolic language, it represents a large group of signs and symbols. There are many mathematical symbols and signs. Without these symbols, it is impossible to carry out specific mathematical operations. Sometimes it is the little things that are the most important. 

Representing the  relationship between numbers symbolically not only helps  to simplify the process but also gives a better understanding of the concept than a wordy description of the same. 

In simpler words,  plus sign, a minus sign, a multiplication sign are all symbols. We need them to express what we are doing in a clear manner. When we are adding it would be pointless to always write out one plus one equals two when we could express this symbolically with 1 + 1 = 2. 

Maths is built mainly by  two things: numbers and symbols. We can find symbols  in simple arithmetic, but in  algebra, geometry, probability, statistics, etc. Decimals and fractions, for example, are symbols of parts of a whole. Without symbols we simply could not perform maths because the biggest part of maths is abstract. How can we try to find the value of ‘X’ in algebra if we don’t use the symbol of ‘X’? It is not possible. It is the same in other parts of maths. 

The symbols in mathematics are an important instrument to  communicate the knowledge effectively. Without symbols we have to write for every calculation long language instructions to describe the whole process.  The symbols used in mathematics are universal. In every country people use almost the same mathematical symbols which make mathematics an universal language. 

We can divide the mathematical symbols into two groups. The first group will contain the so-called technical signs. They substitute the  relationships and mathematical operations that usually can be expressed with words, phrases and even with whole sentences. We remember most of these symbols from our schools, and without being mathematicians, we use them in one way or another in our jobs. The professional mathematicians use many more symbols, but they are dealing with a "Higher" level of mathematics where problems are much more abstract and detached from our real lives. Computer scientists, physicists, engineers, logicians and other professions use these special symbols. However, there is something else - computers are now an active part of our lives, which means that our basic computer skills cannot be achieved without the use of some mathematical signs. This means that working with the computer, we are constantly forced to exercise much of the language of mathematics.

In the second group of mathematical symbols, we will present the numbers. This group deserves our special attention. Numbers are such an enormous cultural and scientific phenomenon and they are a huge part of human history and human civilization in general. It took people a long time to invent and offer signs, which indicate how living and nonliving things around us are increasing quantitatively. This today seems simple and easy, but thousands of years have passed, since  people from different countries and cultures reached consensus on this issue.

I am sure we all have this mathematical and cultural knowledge about the number symbols and we all use them consistently in all areas of our professional and personal lives. 

So let us start with the first group of mathematical signs and symbols. All these signs exist by convention and by tradition for many years. This means that historically mathematicians from around the world have reached an agreement to use these characters with the same content.

Here are some general mathematical symbols:

„+“  „Add“. Sign for adding. Example: 3+7 = 10

„−„  „Subtract“. Sign for subtracting. It is a sign for negative numbers as well. Example: 5−2 = 3

„× “  „Multiply“. Sign for multiplying. Example: 4×3 = 12

„  / ÷“ - „Divide“. Signs for dividing. Example: 20/5 = 4

(…) Brackets. Sign for grouping symbols and operations between them. Example: 2(a − 3).

[…]  Square Brackets. Sign for grouping symbols and operations between them. Example: 2[ a − 3(b + c) ].

„∞“  Represents the concept of infinity. Every combination of numbers is infinite because you can add a new number and another one to the combination of already existing numbers.

„= “  „Equals“. It shows the result. Example: 1+1 = 2.

„≈“  „Approximately equal to“. Example: π 3,14.

„≠“  „Not equal to“. It shows that two numbers are not equal to each other. Example: π ≠ 2.

„< ≤ “  „Less than, Less than or equal to“. We use these signs when we compare numbers. Example: 2 < 3.

„ > ≥“  „Greater than, Greater than or equal to“, We use these signs when we compare numbers. Example: 5 > 1.

„√“  „Square root“. It shows the number multiplied by itself. Example: √4 = 2

„° “  „Degree“. It shows the angle degree and the temperature. Example: 20°.

„⇒“  „If…, then“ . Example: A and B  are  odd numbers ⇒ A + B they give an even number.

„⇔“ "If and only if" or "equivalent to". Example: x=y+1 ⇔ y=x−1.

„%“  „Percent sign“. It is the symbol used to indicate a percentage, a number or ratio as a fraction of 100. Example: % = 1/100.

Let us not forget that today we have the privilege to use all these symbols free. However, generations of mathematicians and logicians worked hard to invent them for us. Some mathematical signs come just from the logic to express certain characteristic relationships. 

We live in a colourful symbolic world. Different signs and symbols surround us every day in different areas. We gradually learn how to understand their language. We gradually learn how to communicate some ideas and knowledge using them. Some of these symbols speak to us in a deep way. The symbol of the red heart for example is universally  acknowledged as a sign of love and warm emotions. Probably because it is agreed between humans that the heart is that special part of our body that is responsible for emotions. Every day we operate with some spiritual symbols as well. The spiritual symbols we use depend on our religious beliefs. 

There is a special relationship between the symbols and humans. The symbols are man made but they have a strong influence on people's lives, it goes both ways.  We put in their creation all our hopes and positive energy gathered through centuries. They become full of our expectations and sacred power. The main spiritual symbols are part of our culture and of the wisdom of our traditions. Often the symbols and the ideas and images they represent are an object of prayers. As a result of that, they carry a magical collective energy that can make any wish come true.  It is something that enriches us and helps us to grow a higher consciousness. The ability to invent symbols and the presence of symbolism in our lives is a great proof that humans have a potential to go closer to the divine. This Is where we belong. 

Here     are some activities for you: Activity 1: Can you give examples where else we can use the symbol of brackets? Activity 2: Can you practise using the sign of percent? Did you use this symbol today during your shopping? Activity 3:  If you have to invent a new symbol for some actions, ideas or processes, what sign would you use? And what  will this symbol stand for?    Activity 4: Why do you think the ring is a symbol for marriage?    What is the meaning?      Activity 5: Can you make a list with some spiritual symbols from your culture?