Number Systems: Naturals, Integers, Rationals, Irrationals, Reals
Introduction to number system
Natural Numbers |
N |
1, 2, 3, 4, 5, …… |
Whole Numbers |
W |
0,1, 2, 3, 4, 5…. |
Integers |
Z |
…., -3, -2, -1, 0, 1, 2, 3, … |
Rational Numbers |
Q |
p/q form, where p and q are integers and q is not zero. |
Irrational Numbers |
Which can’t be represented as rational numbers |
Types of Numbers
- Natural Numbers: Natural numbers are known as counting numbers that contain the positive integers from 1 to infinity. The set of natural numbers is denoted as “N” and it includes N = {1, 2, 3, 4, 5, ……….}
- Whole Numbers: Whole numbers are known as non-negative integers and it does not include any fractional or decimal part. It is denoted as “W” and the set of whole numbers includes W = {0,1, 2, 3, 4, 5, ……….}
- Integers: Integers are the set of all whole numbers but it includes a negative set of natural numbers also. “Z” represents integers and the set of integers are Z = { -3, -2, -1, 0, 1, 2, 3}
- Real Numbers: All the positive and negative integers, fractional and decimal numbers without imaginary numbers are called real numbers. It is represented by the symbol “R”.
- Rational Numbers: Any number that can be written as a ratio of one number over another number is written as rational numbers. This means that any number that can be written in the form of p/q. The symbol “Q” represents the rational number.
- Irrational Numbers: The number that cannot be expressed as the ratio of one over another is known as irrational numbers and it is represented by the symbol ”P”.
- Complex Numbers: The number that can be written in the form of a+bi where “a and b” are the real number and “i” is an imaginary number is known as complex numbers “C”.
- Imaginary Numbers: The imaginary numbers are the complex numbers that can be written in the form of the product of a real number and the imaginary unit “i”.
Number System |
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