Basics Of Real Numbers

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Definition of Real Numbers

Any valid number you think about is a real number. The real numbers include the whole numbers (such as 1, 20, 30), rational numbers (such as 2/3, 0.168, 2.345) and irrational numbers (such as √5, π). The real numbers are the numbers which exists in reality.

Another real numbers definition is that, “Real value is any value that can be plotted on the continuous number line”.

What is a Continuous Number Line?
The continuous number line is nothing but a geometric line that is represented in the graphs. The central position of the continuous number line will point to 0. Towards the left of zero will be -1, -2, -3, and so on. Towards the right of zero will be 1, 2, 3 and many more positive integers. Any point on this line is a real number, be it rational or irrational.

Here is a diagrammatic representation of continuous number line:

What are the Valid Real Numbers?
As already mentioned, the whole numbers, rational numbers and irrational numbers are termed as real numbers. Whole numbers include all the positive and negative integers.

In ...
... simple terms, real numbers are all numbers except infinity and square root of minus one √-1. The square root of minus one is termed as imaginary number. In general, imaginary numbers are those that give a negative result when they are squared. Infinity is an idea that doesn’t have an end. There is no way to measure infinity. For example, the decimal number equivalent of 1/3 is 0.3333333333333333333333…. This is a never ending number. This is an example of imaginary number.

Is Zero a Real Number?
The question “Is 0 a real number?” is in the minds of several people. Few people say that zero is not a real number because it is not positive or negative. Few claim that real numbers have an inverse but zero doesn’t have one. All these are just arguments. The actual fact is that, “Zero is a real number”. This is because:
Zero is an integer. All integers are real numbers.
Zero is a point that can be marked on the continuous line. Any number that can be plotted on the continuous line is a real number.
Hence, there is no doubt that zero is a real number.

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