Can you think of a value that can neither be defined nor estimated but is so crucial to the programming world? Yes, you got it right! Its *infinity*. But do you know that until 2020 there was no proper way to represent infinity in python? We generally used a **larger/small value or a garbage value** to represent infinity.

**Python Infinity is a variable type that is greater than every other numeric value in python. Rather than using any garbage large value as a limit, you can use pre-defined keyword for initializing an infinite value in Python.**

But now we have many different ways to represent infinity. In this article, we will understand why it is essential in Computer Science and how to express it** in python.**

Catalogue

## How to Represent Infinity in Python?

Infinity can be **positive or negative**. The result of any operation of any with infinity like *sum, product, the division is always infinity*. One more important thing is that infinity is still a **float value**. There is no way to represent infinity as an integer. So, let us now know about all the methods we can represent positive and negative infinity.

### a. Using float()

Python is a *dynamic language*, that is why we can use float() to represent infinity.

positive_inf=float('inf') print("positive_inf:",positive_inf) # For negative infinity, put minus in front of positive infinity negative_inf=-float('inf') print("negative_inf:",negative_inf)

positive_inf: inf negative_inf: -inf

### b. Using the math module to represent infinity in python

We can use the math module to represent infinity.

import math # We can use the inf method of the math module pos_infinity=math.inf print(pos_infinity) neg_infinity=-math.inf print(neg_infinity)

inf -inf

### c. Using the Decimal module

import decimal # Using the Decimal function of decimal module positive_inf=decimal.Decimal("inf") negative_inf=-decimal.Decimal("inf") print(positive_inf) print(negative_inf)

Infinity -Infinity

### d. Using the sympy module

from sympy import oo infinity=oo minus_infinity=-oo print(infinity) print(minus_infinity)

oo -oo

### e. Using the Numpy Module

For using the numpy library, we first need to import it using –

pip install numpy

# importing the numpy library and giving alias np import numpy as np infinity=np.inf negative_infinity=-np.inf print(infinity) print(negative_infinity)

inf -inf

## Performing Operations on Infinity in python

### a. Adding and Subtracting a number.

import math infinity = math.inf val=1000 print(infinity+val) print(infinity-val)

inf inf

Whatever number we add or subtract from infinity, we will get infinity.

### b. Multiply and Divide some number with Infinity

import math infinity = math.inf val=1938 print(infinity*val) print(infinity/val)

inf inf

### c. Finding Remainder of a infinity when divides with a number

import math infinity = math.inf val=121212 print(infinity%val)

nan

### d. Checking if a number is infinity using math.isinf()

We can check if a number is infinity using the **isinf()** method of math module.

import math from sympy import oo infinity=oo print(math.isinf(infinity))

True

### e. Are all infinity same?

Let us now check whether the values from each methods are same or not?

import math from decimal import Decimal import numpy as np from sympy import oo infinity=oo inf_floats=float('inf') inf_math=math.inf inf_Decimal=Decimal("inf") inf_np=np.inf print(inf_floats==inf_math) print(inf_floats==inf_Decimal) print(inf_floats==inf_np) print(inf_floats==infinity) # infinity value from sympy is not equal to other infinity values

True True True False

### f. Comparing the Values of python infinity with other values using python max function

Positive Infinity is the** largest number possible and negative infinity is the smallest number.** Let us compare some values with infinity and check whether it is true or not.

import math print(max(math.inf,9999)) print(min(-math.inf,9999))

inf -inf

We can also do something like this-

import math large_value=9999999999 infinity=math.inf if infinity>large_value: print("Infinity is the largest") else: print(large_value,"is larger") small_value=-9999999999 neg_infinity=-math.inf if neg_infinity<large_value: print("Negative Infinity is the smallest") else: print(large_value,"is smaller")

Infinity is the largest Negative Infinity is the smallest

### g. Changing the type of python infinity into integer

Let us try to change the type from float into integer and see what happens.

import math infinity=math.inf int_infinity=int(infinity) print(int_infinity)

Error: cannot convert float infinity to integer

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## Conclusion

The use of infinity in computer science is great. When we want to compare a number with a very large or small number, we generally use infinity. Not only this, **it can be used to measure the performance of different algorithms. It is generally used when we perform computations on a very large scale.**

Try to run the programs on your side and let us know if you have any queries.

*Happy Coding!*