{"id":116512,"date":"2020-08-10T07:58:07","date_gmt":"2020-08-10T07:58:07","guid":{"rendered":"https:\/\/blog.finxter.com\/?p=11665"},"modified":"2020-08-10T07:58:07","modified_gmt":"2020-08-10T07:58:07","slug":"python-infinity","status":"publish","type":"post","link":"https:\/\/sickgaming.net\/blog\/2020\/08\/10\/python-infinity\/","title":{"rendered":"Python Infinity"},"content":{"rendered":"

Infinite \u201c\u221e\u201d is a term derived from the Latin word infinitas<\/em> which means \u201cwithout an end\u201d or \u201cboundless\u201d. Similarly, infinity in python is an undefined value that can either be positive or negative. It comes in handy for measuring and optimizing complex algorithms. <\/p>\n

The positive infinity is used to denote the greatest of all values while the negative infinity is used to denote the least of all values.<\/em><\/strong><\/p>\n

Until now there is no way to represent infinity as an integer. However, in python float values can be used to represent infinite integer values. <\/p>\n

Let\u2019s explore the ways Infinity can be used in python:<\/em><\/p>\n

Method 1: Using float(inf) and float(-inf)<\/h2>\n

Infinity can be a positive or negative value and can be represented by float(inf) and float(-inf) respectively. <\/p>\n

The following code demonstrates the implementation of positive and negative infinity:<\/em><\/p>\n

infinity_positive = float('Inf')\nnumber = 9999999999999999999999999\nif number > infinity_positive: print(\"number is greater than Infinity!\")\nelse: 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)<\/pre>\n
Output:<\/strong><\/p>\n
Positive Infinity is the greatest! Even greater than 9999999999999999999999999 Negative Infinity is the least! Even smaller than -9999999999999999999999999<\/pre>\n
Method 2: Using the \u201cmath\u201d Module<\/h2>\n
Python\u2019s math module can also be used to implement infinity. In Python 3.5 and higher math.inf is a predefined constant that is used to return positive infinity while -math.inf constant returns negative infinity. It returns a floating value.<\/p>\n
The following code demonstrates the implementation of infinity using the math module:<\/em><\/p>\n
import math\ninfinity_positive = math.inf\nnumber = 9999999999999999999999999\n# Positive Infinity\nif number > infinity_positive: print(\"number is greater than Infinity!\")\nelse: print(\"Positive Infinity is the greatest! Even greater than\",number)\n# Negative Infinity\ninfinity_negative = -math.inf\nif -number < infinity_negative: print(\"number is lesser than Negative Infinity!\")\nelse: print(\"Negative Infinity is the least! Even smaller than\",-number)<\/pre>\n
Output:<\/strong><\/p>\n
Positive Infinity is the greatest! Even greater than 9999999999999999999999999 Negative Infinity is the least! Even smaller than -9999999999999999999999999<\/pre>\n
Method 3: Using the \u201cdecimal\u201d module<\/h2>\n
Another way of implementing infinity is by using Python\u2019s decimal module. Decimal(\u2018Infinity\u2019) returns positive infinity while Decimal(\u2018-Infinity\u2019) returns negative infinity.<\/p>\n
The following code demonstrates the implementation of infinity using the math module:<\/em><\/p>\n
from decimal import Decimal\ninfinity_positive = Decimal('Infinity')\nnumber = 9999999999999999999999999 # Positive Infinity\nif number > infinity_positive: print(\"number is greater than Infinity!\")\nelse: print(\"Positive Infinity is the greatest! Even greater than\",number) # Negative Infinity\ninfinity_negative = Decimal('-Infinity')\nif -number < infinity_negative: print(\"number is lesser than Negative Infinity!\")\nelse: print(\"Negative Infinity is the least! Even smaller than\",-number)<\/pre>\n
Output:<\/strong><\/p>\n
Positive Infinity is the greatest! Even greater than 9999999999999999999999999 Negative Infinity is the least! Even smaller than -9999999999999999999999999<\/pre>\n
Method 4: Using the \u201cNumpy\u201d library<\/h2>\n
Another popular way of implementing Infinity in python is by using Python\u2019s famous Numpy library. Numpy has its own definitions for infinite values. np.inf returns positive infinity while -np.inf returns negative infinity.<\/p>\n
The following code demonstrates the implementation of infinity using the math module:<\/em><\/p>\n
import numpy as np\ninfinity_positive = np.inf\nnumber = 9999999999999999999999999\n# Positive Infinity\nif number > infinity_positive: print(\"number is greater than Infinity!\")\nelse: print(\"Positive Infinity is the greatest! Even greater than\",number)\n# Negative Infinity\ninfinity_negative = -np.inf\nif -number < infinity_negative: print(\"number is lesser than Negative Infinity!\")\nelse: print(\"Negative Infinity is the least! Even smaller than\",-number)<\/pre>\n
Output:<\/strong><\/p>\n
Positive Infinity is the greatest! Even greater than 9999999999999999999999999 Negative Infinity is the least! Even smaller than -9999999999999999999999999<\/pre>\n
Infinity Arithmetic<\/h2>\n
Generally, most arithmetic operations performed on infinity values result in generation of other infinite values. The following example illustrates this concept :<\/p>\n
value = float('inf')\nprint('Result of Addition : ',value + 15)\nprint('Result of Subtraction : ',value - 15)\nprint('Result of Multiplication : ',value * 15)\nprint('Result of Division : ',value \/ 15)\n#special scenario\nprint('Multiplication by Zero: ',value * 0)<\/pre>\n
Output:<\/strong><\/p>\n
Result of Addition: inf\nResult of Subtraction: inf\nResult of Multiplication: inf\nResult of Division: inf\nMultiplication by Zero: nan<\/pre>\n
Note:<\/em><\/strong><\/p>\n
    \n
  • Division by zero raises a ZeroDivisionError<\/strong> exception instead of yielding a resultant value.<\/li>\n
  • Arithmetic operations on NaN always give NaN. There is no “negative NaN”.<\/li>\n<\/ul>\n
    Python Infinity Check<\/h2>\n
    The isinf()<\/em><\/strong> method of the math module is used to check for infinite values in python. The following example demonstrates this concept :<\/p>\n
    import numpy as np\nimport math\nnum1 = np.inf\nnum2 = -np.inf\nnum3 = 25\nprint(\"Is num1 an infinite number?: \",math.isinf(num1))\nprint(\"Is num3 an infinite number?: \",math.isinf(num2))\nprint(\"Is num2 an infinite number?: \",math.isinf(num3)) <\/pre>\n
    Creating Arrays with Infinity values<\/h2>\n
    The following example demonstrates how an array of infinity values can be created:<\/p>\n
    import numpy as np\n# To create a numpy array with all values initialized to infinity\narray_infinity = np.full(5, np.inf)\nprint('Infinite Array: ',array_infinity) <\/pre>\n
    Output:<\/strong><\/p>\n
    Infinite Array: [ inf inf inf inf inf]<\/pre>\n
    Test your knowledge based on the above explanations:<\/strong><\/p>\n
    What will be the output of the following snippets?<\/em><\/p>\n