In this section you’ll learn from what did the math start developing as exact science. First thing you need to start dealing with are **numbers**.

### Numbers lessons

An irrational number is a non-terminating, non-repeating decimal. A set of all irrational numbers is denoted by . The examples of rational numbers are . By ...

A linear congruence is an equation of the form Lemma. Solving the congruence is equivalent to solving the linear Diophantine equation . Since ...

The goal of this lesson is to familiarize the reader with the properties of operations of rational numbers, and before that, how we construct and define

The supremum A non-empty set is bounded from above if there exists such that The number is called an upper bound of . If a set is bounded

Let be the point in the complex plane which is join to the complex number . The position of the point , and thus of the complex number , we can determine

Inductive reasoning is reasoning in which on the basis of a series of individual cases we make conclusion about the general rule. However, that conclusion

Operations of addition and multiplication of complex numbers are commutative, associative and distributive. If and are complex numbers, then their

The reason for the introduction of complex numbers is so that every quadratic equation will have a solution. For instance, an equation contains solutions

If we want fully understand numbers and number sets, we must learn how to construct each sets of numbers. Construction of number systems: Natural numbers

The thing you should pay attention to is reducing fractions and shortening expressions...

Every rational equation comes down to a polynomial equation with one important exception.

Separate one complicated fraction into a sum of few smaller ones

Adding and subtracting rational expressions are just like adding and subtracting rational numbers.

To simplify rational expression means the same as simplifying the fraction.

Comparing decimals is the first...

Multiplication of decimals is done in the same way as is the multiplication of integers.

Use them in basic operations like...

The set that contains both positive and negative numbers is called the set of whole numbers or the set of integers and we mark the set with $\mathbb{Z}$.

Multiplication and division of integers or whole numbers is done the same way...

Positive integers you already...

There are three basic forms...

Dividing is used for splitting up something into equal groups. Opposite of multiplication.

Multiplying is brother operation of addition. It is used to add multiple numbers in a group.

Subtracting is opposite of adding. This math opeartion subtract elements one from another.

Adding is the most basic math function that implies combination of two or more objects into larger group.

Of course, as you may guess, numbers are one of the most important things that people came up with in ages. First people used lines as numbers, for counting almost anything. They marked the amount of food they had compared that with numbers they used to mark and then they knew exactly how many food they needed in order to survive long winters or trips. Of course, today we use numbers in many different modern ways. Just try to picture a world without numbers, you would never know what time is it, you wouldn’t know how much something costs, you couldn’t count, measure, almost nothing. If people never came up with an idea of writing the amounts of something or measure things they see, none of the most important sciences would exist today.

For the world we know today it wasn’t enough only to write numbers and possess the knowledge of counting. As the market evolved, trading was replaced with buying and selling goods with coins. For these two operations it was necessary to know how to add and subtract money. As you can imagine, subtracting and adding wasn’t so easy to invent. People used many things that can help them in that process, like abacus or sticks and stones.

Arithmetic evolved a lot through the years, as the need for larger numbers and different operations emerged. As the businesses of people evolved the hierarchy of employers and employees came to be, and the salaries had to be paid. For this, the money earned had to be fairly divided between the workers. For this need, people developed multiplication and division. In one time of history, people knew only of these four operations. Again, this wasn’t enough. When things couldn’t be equally divided into a set number of parts, fractions and decimals came on the stage. Just think how magnificent it is that from these simple operations whole math and the world evolved. Of course, not everything was simple. Everyone that dealt with math had to put everything they had into creating something new. Starting from the scratch is never easy, but think of how their effort made living easier and that with learning what they discovered is benefiting you and enriches your brain.

As your knowledge of mathematics grows, you’ll get to know many different kinds of numbers, some you already know and can find in nature, some less common and some you maybe don’t quite understand why they exist. Don’t worry if you have any questions or doubts, we are here to help.

Come with us on an exciting adventure through the world of numbers and the first steps in understanding everything.