# Python Infinity

## Introduction

We will discover how to define an infinite number in Python in this tutorial. Infinity, as we all know, is a value that cannot be defined and can either be positive or negative. Any arithmetic operation done on an infinite value, including addition, subtraction, multiplication, and division, will always result in an infinite number.

## Python Infinity

Because it has no beginning and hence cannot be represented by an integer, infinity. We are aware that every operation in mathematics that is done on an infinite value will result in an infinite value. The value is displayed as a float. Let's learn about all the ways to represent infinite values, both positive and negative.

The way that numbers are written in Python plays a role in why the infinity data type is a float rather than an int. A binary representation of an integer number is used to represent it; for instance, the value 7 is written as 0111.

However, the float numbers are represented by three components:

### The sign:

It's as straightforward as the name. The representation for a positive number is 0, while the symbol for a negative number is 1.

### The mantissa:

The set of significant digits in a floating-point integer or a scientific notation is known as the mantissa. Here, the only numbers present are O and 1. A mantissa that has just one 1 to the left of the decimal is said to be normalized.

### The exponent:

The exponent field must contain both +ve (positive) and -ve (negative) exponent representations. The real exponent is combined with a bias to get the stored exponent.

This complies with the IEEE 754 specification for a means of storing floating-point numbers. Some values are set aside in the standard to represent special numbers. Infinity is one of these unique numbers.

This standard states that a floating-point integer represents infinity when all of the bits in the exponent and mantissa parts are 1, respectively. Additionally, a sign bit of 1 indicates a negative infinity, while a sign bit of 0 indicates positive infinity.

Since infinity is a unique value, it cannot be represented in a straightforward binary manner. In Python, it has the float datatype instead.

### 1. Using float(‘inf’) and float(‘-inf’):

Infinity can be expressed as a float('inf') or float('-inf') depending on whether it is positive or negative. The implementationof the previously discussed content is shown in the code below:

Code:

``````# Defining an infinite +ve number
positive__infinity = float('inf')
print ('Positive Infinity: ', positive__infinity)

# Defining an infinite -ve number
negative__infinity = float('-inf')
print ('Negative Infinity: ', negative__infinity)
``````

Output:

``````Positive Infinity:  inf
Negative Infinity:  -inf
``````

### 2. Using Python’s math module:

Python's math library can also be used to represent infinite integers. The code below demonstrates how to do it:

Code:

``````import math

# Defining an infinite positive number
positive__infinity = math.inf
print ('Positive Infinity: ', positive__infinity)

# Defining an infinite negative number
negative__infinity = -math.inf
print ('Negative Infinity: ', negative__infinity)``````

Output:

``````Positive Infinity:  inf
Negative Infinity:  -inf``````

### 3. Using Python's decimal module:

The Python decimal module can also be used to express infinite float values.Decimal('Infinity') and Decimal('-Infinity') are used to represent positive and negative infinite values, respectively.

Its implementation is shown in the code below:

Code:

``````from decimal import Decimal

# Defining an infinite positive number
positive__infinity = Decimal('Infinity')
print ('Positive Infinity: ', positive__infinity)

# Defining an infinite negative number
negative__infinity = Decimal('-Infinity')
print ('Negative Infinity: ', negative__infinity)
``````

Output:

``````Positive Infinity:  Infinity
Negative Infinity:  -Infinity``````

### 4. Utilizing the Numpy library for Python

Infinite values can also be represented using the Numpy module in Python. For positive and negative infinite values, it is used as np.inf and -np.inf, respectively. The code below demonstrates how to express an infinite value using the Numpy library:

Code:

``````import numpy as np

# Defining an infinite positive number
positive__infinity = np.inf
print ('Positive Infinity: ', positive__infinity)

# Defining an infinite negative number
negative__infinity = -np.inf
print ('Negative Infinity: ', negative__infinity)``````

Output:

``````Positive Infinity:  inf
Negative Infinity:  -inf``````

### 5. Python Code to Determine whether a Number Is Infinite

The math library's isinf() function, which returns a boolean value, can be used to determine whether a given number is infinite or not. The isinf() method is used in the code below:

Code:

``````import numpy as np
import math

# Defining an infinite positive number
x = np.inf

# Defining an infinite negative number
y = -np.inf

# Define a finite integer
z = 200

# Check if an in infinite
print (math.isinf(x))

# Check if b in infinite
print (math.isinf(y))

# Check if c in infinite
print (math.isinf(z))``````

Output:

``````True
True
False``````

### 6. Procedures in arithmetic on an infinite number

Since infinity is a float value, it can be subjected to a variety of mathematical operations. The IEEE standard also defines the outcomes of these procedures.

Code:

``````# Define positive x value for infinity.
x = float('inf')

# Define negative x value for infinity.
y = float('-inf')

# Working with positive infinity values
print ('For Positive Infinity Value:')
print ('Addition value : ', x + 6)
print ('Subtraction value : ', x - 6)
print ('Multiplication value: ', x * 6)
print ('Division value: ', x / 6)
print ("--------------------------------------------")
# Working with negative infinity values
print ('For Negative Infinity Value:')
print ('Addition value: ', y + 12)
print ('Subtraction value: ', y - 12)
print ('Multiplication value: ', y * 12)
print ('Division value: ', y / 12)``````

Output:

``````For Positive Infinity Value:
Subtraction value :  inf
Multiplication value:  inf
Division value:  inf
--------------------------------------------
For Negative Infinity Value:
Subtraction value:  -inf
Multiplication value:  -inf
Division value:  -inf
``````

### 7. Python comparison of infinite and finite values

It doesn't get any easier than comparing infinite values to finite values. Like how negative infinity is always lower than negative numbers and positive infinity is always greater than any natural integer. Consider the following code for a better understanding:

Code:

``````import numpy as np

# X is defined as a positive, infinite integer.
x = np.inf

# y is defined as a positive, infinite integer.
y = -np.inf

# Define finite z positive integer
z = 200

# Define finite z negative integer
p = -200

# Helper method to make comparisons
def compare (x, y):
if x>y:
print ("True")
else:
print ("False")

compare (x, y)
compare (x, z)
compare (x, p)
compare (y, z)
compare (y, p)
``````

Output:

``````True
True
True
False
False``````