How can I represent an infinite number in python? No matter which number you enter in the program, no number should be greater than this representation of infinity.
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14 Answers
In Python, you can do:
test = float("inf") In Python 3.5, you can do:
import math test = math.inf And then:
test > 1 test > 10000 test > x Will always be true. Unless of course, as pointed out, x is also infinity or "nan" ("not a number").
Additionally (Python 2.x ONLY), in a comparison to Ellipsis, float(inf) is lesser, e.g:
float('inf') < Ellipsis would return true.
2 Comments
quickbug
Note that infinity is defined in the norm IEEE 754-1985 (en.wikipedia.org/wiki/IEEE_754-1985), which Any modern language will rely on. Another point is that, according to this norm, infinity must (obviously) be a floating-point number. This might explain why Python have chosen this akward syntax.
Sergey Zakharov
And you can do
-float("inf") to get minus infinity which is smaller than any other number.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 
3 Comments
stefanbschneider
How do
float("inf"), math.inf, and np.inf compare? Which one to use when?
ajsp
@CGFoX Use the first one if you don't want to load packages, that's about the height of it.
AccidentalTaylorExpansion
@stefanbschneider under the hood they all use the same floating point representation of infinity as specified by the IEEE 754 floating point standard. So they are essentially all the same. On my machine, using timeit,
float('inf') took about 185 nanoseconds, whereas the numpy and math versions both took about 70 nanoseconds. This is probably because float('inf') has to parse the string and perform some checks. This small of a time is almost always too small to optimize for, but since they are also quicker to type, I don't see why you would use the float('inf') optionI don't know exactly what you are doing, but float("inf") gives you a float Infinity, which is greater than any other number.
Comments
There is an infinity in the NumPy library: from numpy import inf. To get negative infinity one can simply write -inf.
2 Comments
stefanbschneider
How do
float("inf"), math.inf, and np.inf compare? Which one to use when?
Lenar Hoyt
The first two are native i.e. require no dependency.
np.inf requires the Numpy package. float('inf') is a bit hacky as it involves parsing a string, but on the upside it does not even require an import and the parsing is typically computationally negligible. If you use one of the math packages anyway, though, then just use them. If you happen to use both math and np, then np.inf is the shortest one.Another, less convenient, way to do it is to use Decimal class:
from decimal import Decimal pos_inf = Decimal('Infinity') neg_inf = Decimal('-Infinity') 
10 Comments
Niccolò
why don't you add why it is less convenient and why anyone should use it?
Denis Malinovsky
Let's see:
Decimal('Infinity') == float('inf') returns True, so it's pretty much the same.
nemesifier
@afzal_SH
float('inf') is float('inf') returns False toonemesifier
infinity is different even from itself, so your comment didn't make much sense to me, IMHO
Manoel Vilela
float('inf') is float('inf') -> False, just holds that they are different objects with different instances, but not that the internal contents are different -- actually as @nemesisdesign pointed float('int') == float('int') holds to True. This is the same problem like comparing mutable objects like [1,2,3] is [1,2,3] and [1,2,3] == [1,2,3], which are, in order, False and True.. More info see: stackoverflow.com/questions/2988017/… |
Infinity
1. Using float('inf') and float('-inf)
positive_infinity = float('inf') negative_infinity = float('-inf') 2. Using Python’s math module
import math positive_infinity = math.inf negative_infinity = -math.inf 3. Integer maxsize
import sys maxSize = sys.maxsize minSize = -sys.maxsize 4. Using Python’s decimal module
from decimal import Decimal positive_infinity = Decimal('Infinity') negative_infinity = Decimal('-Infinity') 5. Using Numpy Library
from numpy import inf positive_infinity = inf negative_infinity = -inf 
1 Comment
WestCoastProjects
Upvoted for the
sys.maxsize since we often want integers . I wish they had named it maxint instead so it would be easier to rememberIn 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() answered Nov 8, 2014 at 10:07
Antony Hatchkins
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2 Comments
Ali Rasim Kocal
If you really have yo use this, at least wrap it in some readable names like:
MIN_INFINITY = None; INFINITY = "inf"; MIN_INFINITY < x < INFINITY
Joost
But you don't have to use this.
Also if you use SymPy you can use sympy.oo
>>> from sympy import oo >>> oo + 1 oo >>> oo - oo nan etc.
Comments
For Positive Infinity
pos_inf_val = float("infinity") For Negative Infinity
neg_inf_val = float("-infinity") 
Comments
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 Comments
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") 
Comments
Use:
float('inf') Or the math module:
import math math.inf But if you print it, they will both return inf, which proves that math uses float('inf') as well.
Comments
For anyone who needs to define his own concept of a number, you could create your own class:
class Infinity(object): # equivalence def __eq__(self, other): return False # negation def __ne__(self, other): return False # less than def __lt__(self, other): return False # less than or equal def __le__(self, other): return False # greater than def __gt__(self, other): return False # greater than or equal def __ge__(self, other): return False Usage:
y = Infinity() x = -99999999999999999999 print(y > x) # False print(y < x) # False 
math.infis useful as an initial value in optimisation problems, because it works correctly with min, eg.min(5, math.inf) == 5. For example, in shortest path algorithms, you can set unknown distances tomath.infwithout needing to special caseNoneor assume an upper bound9999999. Similarly, you can use-math.infas a starting value for maximisation problems.There should be one-- and preferably only one --obvious way to do it.mathstandard library or by asking thefloattype to parse the string"inf".