Handling infinity in programming languages

Note#49

notes
Published

2023-03-24

In Python, infinity (inf) and negative infinity (-inf) are special floating-point values representing numbers larger or smaller than any other number, respectively. They can be the result of certain mathematical operations, such as dividing a positive number by zero for infinity or dividing a negative number by zero for negative infinity. To represent infinity in Python, use the constant float("inf"), and for negative infinity, use float("-inf").

In the NumPy library, which is widely used in Python for numerical computations, infinity can be represented using the np.inf or np.PINF constants, and negative infinity can be represented using the -np.inf or np.NINF constant:

import numpy as np
inf = np.inf  # or inf = np.PINF
neg_inf = np.NINF  # or neg_inf = -np.inf

In C++, infinity and negative infinity can be represented using the std::numeric_limits library from the header:

#include <limits>
double inf = std::numeric_limits<double>::infinity();
double neg_inf = -std::numeric_limits<double>::infinity();

Mathematical operations involving inf and -inf follow specific rules:

  1. Any number added to or subtracted from inf results in inf. For -inf, the same operation results in -inf.
  2. Any positive number multiplied by inf results in inf, and by -inf results in -inf.
  3. Any negative number multiplied by inf results in -inf, and by -inf results in inf.
  4. Dividing any number by inf or -inf results in 0.
  5. Some operations with inf and -inf are undefined or considered not a number (NaN), such as dividing inf by inf, dividing -inf by -inf, or adding inf and -inf.

Handling infinity is a concept present in multiple programming languages and libraries, allowing for the representation of values larger or smaller than any other number and proper handling of certain mathematical operations.