# Python Infinity

Summary: Python Infinity is an undefined value (negative or positive) such that positive infinity is greater than while negative infinity is lesser than any other value in a given code. The numerous ways of using Python infinity are:

• Using `float('Inf')` and `float('-Inf')`
• Using the `math` module.
• Using the `decimal `module.
• Using the “Numpy” library.
• Using The Inifinity module.

Exercise: Try to find a number that’s greater than infinity! 😉

## Overview

Infinite is a term derived from the Latin word ‘infinitas’ which means “without an end” or “boundless”. Similarly, infinity in Python is an undefined value that can either be positive or negative.

☞ Here’s a thumb rule about Python Infinity:

Positive Infinity > Any other value in a python code > Negative Infinity

Until now there is no way to represent infinity as an integer. However, you might want to have a look at the ways in which an integer value can be made greater than any other value in this Blog Tutorial.

Let’s explore the ways Infinity can be used in Python:

## Method 1: Using float(‘Inf’) And float(‘-Inf’)

Infinity can be a positive or negative value as we mentioned in our thumb rule.

1. `float('Inf')` is used to represent positive infinity.
2. `float('-Inf')` is used to represent negative infinity.

The following code demonstrates the implementation of positive and negative infinity:

```infinity_positive = float('Inf')
number = 9999999999999999999999999
if number > infinity_positive:
print("number is greater than Infinity!")
else:
print("Positive Infinity is the greatest! Even greater than",number)
infinity_negative = float('-Inf')
if -number < infinity_negative:
print("number is lesser than Negative Infinity!")
else:
print("Negative Infinity is the least! Even smaller than",-number)```

Output:

```Positive Infinity is the greatest! Even greater than 9999999999999999999999999
Negative Infinity is the least! Even smaller than -9999999999999999999999999```

## Method 2: Using Python Math Module

Python’s math module can also be used to implement infinity in Python 3.5 and above.

1. `math.inf` is a predefined constant in Python that returns positive infinity.
2. `-math.inf` is a predefined constant in Python that returns negative infinity.

The following code demonstrates the implementation of infinity using the math module:

```import math
infinity_positive = math.inf
number = 9999999999999999999999999
# Positive Infinity
if number > infinity_positive:
print("number is greater than Infinity!")
else:
print("Positive Infinity is the greatest! Even greater than",number)
# Negative Infinity
infinity_negative = -math.inf
if -number < infinity_negative:
print("number is lesser than Negative Infinity!")
else:
print("Negative Infinity is the least! Even smaller than",-number)```

Output:

```Positive Infinity is the greatest! Even greater than 9999999999999999999999999
Negative Infinity is the least! Even smaller than -9999999999999999999999999```

## Method 3: Using The Decimal Module

Another way of implementing infinity is by using Python’s decimal module which helps us to deal with fixed and floating-point arithmetic in Python.

1. `Decimal(‘Infinity’)` returns positive infinity.
2. `Decimal(‘-Infinity’) `returns negative infinity.

The following code demonstrates the implementation of infinity using the `math` module:

```from decimal import Decimal
infinity_positive = Decimal('Infinity')
number = 9999999999999999999999999

# Positive Infinity
if number > infinity_positive:
print("number is greater than Infinity!")
else:
print("Positive Infinity is the greatest! Even greater than",number)

# Negative Infinity
infinity_negative = Decimal('-Infinity')
if -number < infinity_negative:
print("number is lesser than Negative Infinity!")
else:
print("Negative Infinity is the least! Even smaller than",-number)```

Output:

```Positive Infinity is the greatest! Even greater than 9999999999999999999999999
Negative Infinity is the least! Even smaller than -9999999999999999999999999```

## Method 4: Using The “Numpy” Library

Another popular way of implementing Infinity in Python is by using Python’s Numpy library. Numpy has its own definitions for infinite values.

1. `np.inf` returns positive infinity.
2. `-np.inf` returns negative infinity.

The following code demonstrates the implementation of infinity using the math module:

```import numpy as np
infinity_positive = np.inf
number = 9999999999999999999999999
# Positive Infinity
if number > infinity_positive:
print("number is greater than Infinity!")
else:
print("Positive Infinity is the greatest! Even greater than",number)
# Negative Infinity
infinity_negative = -np.inf
if -number < infinity_negative:
print("number is lesser than Negative Infinity!")
else:
print("Negative Infinity is the least! Even smaller than",-number)```

Output:

```Positive Infinity is the greatest! Even greater than 9999999999999999999999999
Negative Infinity is the least! Even smaller than -9999999999999999999999999```

## Method 5: Using The Inifinity Module

The all-in-one infinity value module designed by Konsta Vesterinen can be compared to any object. That means it overcomes the limitations of being able to compare only float values. When we try to compute` pow(1, float('inf'))` returns 1. Frankly speaking, this should not be the case, as it should be undefined. When you use the infinity module it returns a `type error` in this case instead of returning 1 which is more acceptable and realistic.

Since infinity is not a part of Python’s standard library. So, before using it, you must install it using the following command:

`pip install infinity`

Let us have a look at the following code to understand how the Infinity class works:

```from infinity import inf

number = 9999999999999999999999999

# Positive Infinity
if number > inf:
print("number is greater than Infinity!")
else:
print("Positive Infinity is the greatest! Even greater than",number)

# Negative Infinity
infinity_negative = -inf
if -number < infinity_negative:
print("number is lesser than Negative Infinity!")
else:
print("Negative Infinity is the least! Even smaller than",-number)```

Output

```Positive Infinity is the greatest! Even greater than 9999999999999999999999999
Negative Infinity is the least! Even smaller than -9999999999999999999999999```

Having learned numerous ways of implementing infinity in python, let us have a look at few operations that can be performed using python infinity.

## Infinity Arithmetic

Generally, most arithmetic operations performed on infinity values result in generation of other infinite values. The following example illustrates this concept :

```value = float('inf')
print('Result of Addition : ',value + 15)
print('Result of Subtraction : ',value - 15)
print('Result of Multiplication : ',value * 15)
print('Result of Division : ',value / 15)
#special scenario
print('Multiplication by Zero: ',value * 0)```

Output:

```Result of Addition:  inf
Result of Subtraction:  inf
Result of Multiplication:  inf
Result of Division:  inf
Multiplication by Zero:  nan```

Note:

• Division by zero raises a` ZeroDivisionError` exception instead of yielding a resultant value.
• Arithmetic operations on `NaN` always give `NaN`. There is no “negative NaN”.

## Python Infinity Check

The `isinf()` method of the math module is used to check for infinite values in Python. The following example demonstrates this concept :

```import numpy as np
import math
num1 = np.inf
num2 = -np.inf
num3 = 25
print("Is num1 an infinite number?: ",math.isinf(num1))
print("Is num3 an infinite number?: ",math.isinf(num2))
print("Is num2 an infinite number?: ",math.isinf(num3)) ```

## Creating Arrays With Infinity Values

The following example demonstrates how an array of infinity values can be created:

```import numpy as np
# To create a numpy array with all values initialized to infinity
array_infinity = np.full(5, np.inf)
print('Infinite Array: ',array_infinity) ```

Output:

`Infinite Array:  [ inf  inf  inf  inf  inf]`

Test your knowledge based on the above explanations:

What will be the output of the following snippet?

```import math

a=float('-infinity')
b=float('inf')
print(a)
print(b)
print(math.inf)
print(-math.inf)```

## Why Use Python Infinity?

Infinity is majorly used in complex algorithmic designs and optimization problems. One such example is the Shortest Path Algorithm where the current distance values have to be compared with the best or the least distance values. It is extremely useful in comparison scenarios where it acts as an unbounded upper or lower value.

Let us have a look at a simple program that finds the cheapest path from a list of given options:

```least_path_cost = float('inf')
# Assume that these values were calculated using some xyz algorithm
path_cost = [10, 100, 99999999999, 50]
for path in path_cost:
if path < least_path_cost:
least_path_cost = path
print("The Lowest Path is", least_path_cost)```

Output

`The Lowest Path is 10`

If we did not have the positive infinity i.e.` float(inf)` available to us, we would not have known the initial lowest_path_cost value in the code. Thus we see the importance of `infinity `in python.

## Conclusion

In this article, we covered numerous ways of dealing with Python infinity and I hope you found this article useful and it helps you to get started with the fundamentals of Python Infinity!

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