In the world of numbers, any number that comes in your mind is the real number. A real number may be a whole number, natural number, integer, fraction, rational number, or an irrational number, and it ranges from a positive integer to a negative integer. However, any imaginary number or infinity is excluded from the list of Real Numbers. We can express a real number using a straight line.

Also Read: Number system

Why do we call them real numbers?

Well, the answer might sound stupid, but, in this case,  real numbers are ‘real’ numbers because they are not ‘imaginary’ numbers. The answer is not related to any reference related to the ‘real’ world, or whatsoever, and a set of real numbers is symbolized by using an “R”.

The sets of positive real numbers are denoted by using R+, and the negative sets are denoted by using R-.

A set of real numbers is numerous and uncountable, and all of the sets are infinite sets. However. ironically, infinity is not a real number. 

Any real number follows several properties in mathematics and physics. To find out, go through the properties elaborated below.

1. Non-zero real numbers are either negative or positive, as there is no middle point.
2. The sum and product of a couple of positive real numbers give the result of another positive real number.
3. Real numbers make an infinite set of numbers.
4. Real numbers can be used to elaborate on the measurements of continuous elements.
5. Real numbers are inseparable because of the dense uncountable set of numbers making them locally compact.

One of the best properties of a real number is the limitation. If said on point, a sequence of real numbers has a limit, and the sequence is termed as the “Cauchy Sequence”. The other properties of real numbers are their uncountability that states that there are more real numbers than natural numbers., even if both of the sets are equal.

Zero is considered to be both real and imaginary, as imaginary numbers are the square roots of non-positive real numbers (√-3), and Zero is a non-positive number. Thus, zero is an imaginary number. However, zero is also a rational number that can be elaborated using the straight line. Thus, it is also a real number. 

The real number is a subset of the complex number, and a complex number is the combination of both the real and imaginary sections (3+4j).

The concept of real numbers is a known concept in the world of computer application through coding. In coding, the compiler assigns a certain value to each data type on which it functions, and the numbers can be in the form of integer or floating-point. The processor of the computer may use a different kind of logic to perform the calculation on real numbers, Whereas, to process the float value the computer uses a different part of CPU known as FPU. Computers can process all kinds of real numbers and irrational numbers and can modify the calculations accordingly. Thus, real numbers can be explained through various aspects of education or technology. 

Also Read: Even Numbers

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