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Is infinity a number?

  • Last Updated : 29 Sep, 2021

The Number System is a system for representing numbers on the Number Line using a collection of symbols and rules. These symbols, which range from 0 to 9, are referred to as digits. The Number System is used to accomplish mathematical computations ranging from complex scientific calculations to simple counting of Toys for a Kid or the number of chocolates left in the box. Numerous types of number systems exist, each with a different base value for its digits.


Integers are the consists of Whole Numbers including negative values of the Natural Numbers. Fraction numbers are not included in integers, hence they cannot be represented in p/q form. The range of Integers is from the Infinity at the Negative end and Infinity at the Positive end, including zero. 

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Real numbers are numbers that can be represented in decimal form. These numbers include whole numbers, integers, fractions, etc. All the integers belong to Real numbers but all the real numbers do not belong to the integers.

Is infinity a number?

Numbers are limitless, but infinity is not a number. Infinity is a concept rather than a number. Infinity is not a numerical value. A number denotes a quantity, but infinity denotes the absence of a quantity. It implies “continues indefinitely.” That’s exactly what numbers do. They go on and on indefinitely. Infinity could be represented using the symbol ∞. 

  • Infinity has no end

The concept of infinity refers to something that has no end. Example picture journeying indefinitely, attempting to reach infinity. Consider the words “endless” or “boundless.” When there is no reason for something to come to a halt, it is endless.

  • Infinity does not increase

Infinity isn’t “becoming bigger,” it’s already complete. It “goes on and on,” which implies that it is progressing in some way. Infinity, on the other hand, does not do anything; it simply exists.

  • Infinity is not a real number

Infinity is a concept, not a real number. Something without a beginning or an end. It is impossible to quantify infinity. Infinity cannot be measured. 

Sample Problems

Question 1: Does infinity belong to real numbers?


No. Infinity is not a real number.

Question 2: Why is zero a number but infinity is not?


Infinity is an idea of limitless increase to a greater and larger number, but not a discrete value, whereas zero 0 is a discrete number. Because any written number that can be identified as the greatest of numbers can be multiplied by one to become a discrete value. As a result, infinity cannot be expressed as a discrete value and so is not a number.

Question 3: What is an Irrational Number?


Any Number that can not be written in the form of a/b (where a and b are integers & q is not equal to 0) are known as Irrational number.

Question 4: What is Reciprocal of a Number?


Interchanging the Numerator and Denominator of any fraction i.e. If 57/8 then it’s reciprocal is 8/7.

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