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Numbers are defined as mathematical identities that measure, count, or label items. Egyptians were the first to invent the number system. The Roman number system, a unique combination of Roman alphabets, was popular in Europe until the 14th century. Thereafter, the Hindu-Arabic number system was invented and is widely used to date. This number system is widely accepted because of the concept of the symbol 0. The number 0 was conceived by Indian mathematicians around 500 AD, which increased the popularity and wide acceptance of this type of number system. According to the Hindu-Arabic number system, the different types of numbers include rational numbers, irrational numbers, and many more.
Characteristics of Numbers
- Numbers are classified into sets known as the number system
- There are different number systems with different characteristics
- There are different types of numbers known in mathematics
Different Types of Numbers
The numbers are further divided into 2 major types: Real numbers and Imaginary numbers.
- Real numbers are represented by the capital letter R. They represent all types of numbers used for measuring. Real numbers generally include both positive and negative real numbers. Most real numbers contain a decimal point and are regarded as decimal numbers or decimals. A finite number of decimal digits generally expresses these numbers only for rational numbers, and the fractional part has a denominator with its factor being 2 or 5 or both. A real number that is not rational is regarded as an irrational number.
- Imaginary numbers are equal to the product of a real number and imaginary unit i. It is the square root of -1.
Real Numbers
Natural numbers: A natural number is also known as the whole number and includes common numbers like 1,2,3, etc. Initially, 0 was not regarded as a natural number, but after the 19th century, 0 also became a part of natural numbers. The set of natural numbers is denoted by the capital alphabet N; it can also be written as N0 or N1, indicating the starting number is 0 or 1, respectively.
- Integers: The word integer is derived from the Latin word meaning “whole”. This number can be expressed without a fractional component. Integers include 0 and are denoted by the capital alphabet Z. There are positive integers and negative integers. The alphabet Z is represented in different ways to denote different types of integers: Z+, is used for denoting positive integers, Z- denotes negative integers, whereas Z≠0 is used for non-zero integers.
- Rational numbers: These numbers can be expressed as a fraction with an integer numerator and a positive integer denominator. A fraction is written as 2 integers, mainly a numerator and a denominator with a dividing bar in between the two. It is denoted by the capital alphabet Q and is expressed as a ratio of an integer to a non-zero integer. It would be correct to say that all integers are rational numbers, but all rational numbers are not an integer.
- Irrational numbers: Numbers that cannot be expressed as the ratio of 2 integers are regarded as irrational numbers. For example, square root of number 2, logarithms, and many more.
Imaginary Numbers
- Complex numbers: These numbers generally consist of 2 parts: the real part and the imaginary part. The imaginary part is denoted by i, which has the numerical value of the square root of -1. This was assigned by Leonhard Euler. The complex number is represented as x + yi, where x and y are real numbers, and i is the imaginary number. Also, the x part is regarded as the real part, whereas the y part is regarded as the imaginary part as it is multiplied with i, which is the imaginary unit. If the real part of the number is 0, then it would be regarded as an imaginary number. A complex number is represented by the symbol C, and real numbers are a subset of complex numbers.
Real-life uses of numbers
There are various real-life uses of numbers:
- Dial a friend or family member or a friend using the mobile phone.
- Calculating the income, expense, and daily budget of our day-to-day life.
- Application for anything related to proportion and percentage, such as cooking.
- Weigh fruits, vegetables, or any other items from the market.
- The use of elevators to go to floors.
- Calculating the time spent on any particular activity.
- Seeing or determining the time.
- Calculating the profit and loss in a business.
Conclusion
Numbers are defined as mathematical identities used to measure, count, or label items. The system of writing numbers to express it is known as the number system and was first invented by the Egyptians. In the 14th century, the invention of the Hindu-Arabic number system gave the world the concept of 0. This has led to its widespread application worldwide. According to the Hindu-Arabic number system, there are different types of numbers like rational numbers, irrational numbers, complex numbers, real numbers, integers, and many more. All the numbers have their real-life uses.
