# Number

**What does number mean?**- A
**number**is an abstract unit used to specify a multitude. - In modern mathematics, where the size is not specified, the number of objects that have similar characteristics to those of traditional numbers are also called numbers. Numbers are used to indicate numbers in writing.

**Classification of numbers, number system****Numbers can be categorized into clusters:**

**Counting numbers**- Counting counts are defined as a set of representations given by the amount of elements within them, rather than describing the elements of a congregation different from idle in terms of scarcity or multiplicity. The name given to the representatives is called the canonical representative. Each count is a canonical representation at the same time. The absence of a zero in counting numbers is due to the fact that there is no element to represent in the empty nest.

**Natural numbers**- Natural numbers are numbers starting from 0 and going to eternity. In mathematics, the set of natural numbers is denoted by N. The natural number name comes from the idea that these numbers are the numbers we see and recognize in nature. The set of natural numbers is “0” and all positive numbers are the same.

**Integers**- The whole numbers go from minus infinity to plus infinity. That is, “0” extends from the sides to the infinity. The set of complete numbers is denoted by Z.

**Positive integers**- Whole numbers with the “+” sign at the beginning or without anything take the name of the positive integers. They are placed on the right side of 0 in the number axis (in the number direction). All counting numbers are positive integers. The set of positive integers is denoted by Z + and is defined as follows:

**Negative integers**- Whole numbers with a “-” at the beginning are called negative integer numbers. They are located to the left of 0 on the number axis. The set of negative integers is denoted by Z-. Extraction in algebra is expressed as the addition of these numbers to other full numbers.

**Zero**- Zero (0) is not a negative or positive integer. It is a compromise point. It is not included in any of these two clusters. However, exact numbers can also be defined as follows:

**Rational numbers**- Ratio numbers or rational numbers are called magnitudes that correspond to the ratios created using integers. That is, a and b are called rational numbers of numbers in the form a / b, not an integer and zero. Rational numbers are denoted by Q. Rational numbers can be expressed as fractions or decimal numbers: 1/3, 4,25, etc.

**Irrational numbers**- Non-operative numbers or irrational numbers are numbers that can not be written as a / b. Q ‘cluster. The most known member of this set is pi. No proportionate number is included in a disjoint set of numbers. Likewise, any disproportionate number is not included in the set of numbered numbers.

**Reel numbers (R)**- The combination of the set of irrational numbers and the set of rational numbers forms a set of real numbers. This is also called real numbers or real numbers. Geometrides were included in the concept of numbers by Pythagoras and students in common Greek terms during the Classical Greek Period in order to make sense of some of the magnitudes encountered. According to the accounts, Pythagoras said that all the greats in the nature could be expressed by rational numbers. But the hypotenuse he found matched a value such as x ^ {2} = 2 as a result of equality. For many years he claimed to have been able to express such numbers with long fractions, though he was persuaded that one of his students could not prove that such numbers could not be shown in a fractional fashion, but for life he worked to hide it as a secret and continued to say that real numbers were not in the nature .
- Real numbers are used to represent solutions of a set of polynomials whose coefficients are integers or rational numbers. In this sense, the set of real numbers is an object expansion of a set of polynomials with integer coefficients Z [x].
- The set of real numbers is denoted by the letter R.

**Complex numbers**- To solve all algebraic equations, complex numbers or sets of complex numbers are obtained if the real numbers are expanded again. The symbol of the complex numbers is C. They were added to the number concept as an extension of the progress of the solution methods of algebraic equations in the Renaissance period. Unreal numbers come from the square root of the number -1, which is not in the set of real numbers. This number is indicated by the symbol “i” and the square is assumed to be -1.

**Classification summary**- In mathematical notation all symbols above are written in capital letters and bold.