Definition of Number System
It’s a number is a mathematical object used to count, label, and measure.
A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (telephone numbers), for ordering (serial numbers), and for codes (e.g., ISBNs).
Natural Number
The natural numbers are those used for counting and ordering. Like there are six coins on the table and there are more chairs than tables.
Also we can say, only positive round figures are the Natural Number. It’s denoted by “N”.
Example: 1, 2, 3, 4, 5
Integer
An integer is a number that can be written without a fractional or decimal component.
For example, 21, 4, and −2048 are integers; 9.75, 5½, and √2 are not integers. The set of integers is a subset of the real numbers, and consists of the natural numbers (0, 1, 2, 3 …) and the negatives of the non-zero natural numbers (−1, −2, −3 …).
It’s denoted by “I”.
Prime Number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because only 1 and 5 evenly divide it, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6.
It’s denoted by “P”.
Rational Number
A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q is not equal to zero. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by boldface “Q”.
It’s also a recurring/repeatedly number.
Irrational Number
An irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers and b is non-zero.
Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals.
It’s denoted by “Ri”
It’s also a non-recurring number.
Real Number
A real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356… the square root of two, an irrational algebraic number) and π (3.14159265…, a transcendental number).
It’s denoted by “R”.
Imaginary Number
An imaginary number is a number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i^2=-1. An imaginary number has a negative or zero square. For example, 5 i is an imaginary number, and its square is -25. It’s denoted by “i”.
Also we can say square root of any negative numbers is the imaginary number.
Complex Number
It’s the composition of Real Numbers & Irrational Numbers.
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, where i2 = −1. In this expression, a is the real part and b is the imaginary part of the complex number.
Source: Wikipedia
