Python infinity

• Difficulty Level : Easy
• Last Updated : 10 Sep, 2021

As ironic as it may seem infinity is defined as an undefined number that can either be a positive or negative value. All arithmetic operations performed on an infinite value always lead to an infinite number, say it be sum, subtraction, multiplication, or any other operation.
In the world of computer science, infinity is generally used to measure performance and optimize algorithms that perform computations on a large scale application.

Representing infinity as an Integer in python
The concept of representing infinity as an integer violates the definition of infinity itself. As of 2020, there is no such way to represent infinity as an integer in any programming language so far. But in python, as it is a dynamic language, float values can be used to represent an infinite integer. One can use float(‘inf’) as an integer to represent it as infinity. Below is the list of ways one can represent infinity in Python.

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

As infinity can be both positive and negative they can be represented as a float(‘inf’) and float(‘-inf’) respectively. The below code shows the implementation of the above-discussed content:

Python3

 `# Defining a positive infinite integer` `positive_infinity ``=` `float``(``'inf'``)` `print``(``'Positive Infinity: '``, positive_infinity)`   `# Defining a negative infinite integer` `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 module can also be used for representing infinite integers. The below code shows how it is done:

Python3

 `import` `math`   `# Defining a positive infinite integer` `positive_infinity ``=` `math.inf` `print``(``'Positive Infinity: '``, positive_infinity)`   `# Defining a negative infinite integer` `negative_infinity ``=` `-``math.inf` `print``(``'Negative Infinity: '``, negative_infinity)`

Output:

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

3. using Python’s decimal module:

Python’s decimal module can also be used for representing infinite float values.
It is used as Decimal(‘Infinity’) for positive and Decimal(‘-Infinity’) for negative infinite value.

The below code shows its implementation:

Python3

 `from` `decimal ``import` `Decimal`   `# Defining a positive infinite integer` `positive_infinity ``=` `Decimal(``'Infinity'``)` `print``(``'Positive Infinity: '``, positive_infinity)`   `# Defining a negative infinite integer` `negative_infinity ``=` `Decimal(``'-Infinity'``)` `print``(``'Negative Infinity: '``, negative_infinity)`

Output:

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

4. using Python’s Numpy library:

Python’s Numpy module can also be used for representing infinite values. It is used as np.inf for positive and -np.inf for negative infinite value. The use of Numpy library for representing an infinite value is shown in the code below:

Python3

 `import` `numpy as np`   `# Defining a positive infinite integer` `positive_infinity ``=` `np.inf` `print``(``'Positive Infinity: '``, positive_infinity)`   `# Defining a negative infinite integer` `negative_infinity ``=` `-``np.inf` `print``(``'Negative Infinity: '``, negative_infinity)`

Output:

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

Checking If a Number Is Infinite in Python
To check if a given number is infinite or not, one can use isinf() method of the math library which returns a boolean value. The below code shows the use of isinf() method:

Python3

 `import` `numpy as np` `import` `math`   `# Defining a positive infinite integer` `a ``=` `np.inf`   `# Defining a negative infinite integer` `b ``=` `-``np.inf`   `# Define a finite integer` `c ``=` `300`   `# check if a in infinite` `print``(math.isinf(a))`   `# check if b in infinite` `print``(math.isinf(b))`   `# check if c in infinite` `print``(math.isinf(c))`

Output:

```True
True
False```

Comparing infinite values to finite values in python
The concept of comparing an infinite value to finite values is as simple as it gets. As positive infinity is always bigger than every natural number and negative infinity is always smaller than negative numbers. For better understanding look into the code below:

Python3

 `import` `numpy as np`   `# Defining a positive infinite integer` `a ``=` `np.inf`   `# Defining a negative infinite integer` `b ``=` `-``np.inf`   `# Define a finite + ve integer` `c ``=` `300`     `# Define a finite -ve integer` `d ``=` `-``300`   `# helper function to make comparisons` `def` `compare(x, y):` `    ``if` `x>y:` `        ``print``(``"True"``)` `    ``else``:` `        ``print``(``"False"``)` `        `  `compare(a, b)` `compare(a, c)` `compare(a, d)` `compare(b, c)` `compare(b, d)`

Output:

```True
True
True
False
False```

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