How Can I Represent an Infinite Number in Python?

Since Python 3.5 you can use math.inf:

>>> import math
>>> math.inf
inf

No one seems to have mentioned about the negative infinity explicitly, so I think I should add it.

For negative infinity:

-math.inf

For positive infinity (just for the sake of completeness):

math.inf

I don't know exactly what you are doing, but float("inf") gives you a float Infinity, which is greater than any other number.

There is an infinity in the NumPy library: from numpy import inf. To get negative infinity one can simply write -inf.

Another, less convenient, way to do it is to use Decimal class:

from decimal import Decimal
pos_inf = Decimal('Infinity')
neg_inf = Decimal('-Infinity')

In python2.x there was a dirty hack that served this purpose (NEVER use it unless absolutely necessary):

None < any integer < any string

Thus the check i < '' holds True for any integer i.

It has been reasonably deprecated in python3. Now such comparisons end up with

TypeError: unorderable types: str() < int()

Also if you use SymPy you can use sympy.oo

>>> from sympy import oo
>>> oo + 1
oo
>>> oo - oo
nan

etc.

For Positive Infinity

pos_inf_val = float("infinity")

For Negative Infinity

neg_inf_val = float("-infinity")

Representing ∞ in python

float("inf") or float("INF") or float("Inf") or float("inF") or float("infinity") or float("Infinity") creates a float object holding ∞

You can also represent -∞ in python

float("-inf") or float("-INF") or float("-Inf") or float("-infinity") creates a float object holding -∞

You can perform arithmetic operations:

infinity = float("inf")
ninfinity = float("-inf")
nan = float("nan")

print(infinity*infinity)#inf
print(ninfinity+infinity)#not a number
print(1/-infinity)#is -0.0
print(nan*nan)# is not a number
print(1/infinity) # is 0.0 since 1/∞ is 0

Output:

$ python3 floating.py
inf
nan
-0.0
nan
0.0

In Summary, there is two kinds definition for Infinity.

For Positive Infinity

posVal1 = math.inf
posVal2 = float("inf")

For Negative Infinity

negVal1 = -math.inf
negVal2 = float("-inf")