How can I represent an infinite number in Python?

Question

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.

`math.inf` is 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 to `math.inf` without needing to special case `None` or assume an upper bound `9999999`. Similarly, you can use `-math.inf` as a starting value for maximisation problems. — Colonel Panic, Oct 12 '16 at 10:59
In most cases, an alternative to using math.inf in optimization problems is to start with the first value. — Tobias Bergkvist, May 30 '20 at 07:26
Can't help but wonder how so many Python question seems to attract a multitude of ways to do the same thing. How is that Pythonian or compatible with Zen of Python.... — nyholku, Oct 25 '21 at 14:25
@nyholku agree.. `There should be one-- and preferably only one --obvious way to do it.` — Sнаđошƒаӽ, Feb 10 '22 at 01:17
@nyholku It looks to me like the answers here are all substantively suggesting doing the same thing, though. Floating-point infinity is the same built-in object whether you access it as a constant in the `math` standard library or by asking the `float` type to parse the string `"inf"`. — Karl Knechtel, Jun 02 '23 at 01:32

WilHall · Accepted Answer · 2015-10-16T13:15:57.713

927

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.

edited Oct 16 '15 at 13:15

answered Oct 15 '11 at 23:09

WilHall

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Note that infinity is defined in the norm IEEE 754-1985 (http://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. – quickbug Mar 05 '15 at 12:00
3

And you can do `-float("inf")` to get minus infinity which is smaller than any other number. – Sergey Zakharov Jan 06 '21 at 11:16

score 111 · Answer 2 · answered May 10 '15 at 21:49

111

Since Python 3.5 you can use math.inf:

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

answered May 10 '15 at 21:49

Sнаđошƒаӽ · Answer 3 · 2021-02-16T03:59:34.470

98

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

edited Feb 16 '21 at 03:59

answered Dec 09 '16 at 06:31

Sнаđошƒаӽ

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How do `float("inf")`, `math.inf`, and `np.inf` compare? Which one to use when? – stefanbschneider Mar 30 '22 at 07:01
3

@CGFoX Use the first one if you don't want to load packages, that's about the height of it. – ajsp Jul 14 '22 at 09:53

score 34 · Answer 4 · answered Oct 15 '11 at 23:09

34

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

answered Oct 15 '11 at 23:09

Ned Batchelder

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score 33 · Answer 5 · answered May 05 '16 at 22:35

33

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

answered May 05 '16 at 22:35

Lenar Hoyt

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How do `float("inf")`, `math.inf`, and `np.inf` compare? Which one to use when? – stefanbschneider Mar 30 '22 at 07:01
1

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. – Lenar Hoyt Mar 30 '22 at 16:33

score 27 · Answer 6 · answered Oct 12 '13 at 03:53

27

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

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

answered Oct 12 '13 at 03:53

Denis Malinovsky

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why don't you add _why it is less convenient and why anyone should use it_? – Niccolò Jul 25 '14 at 11:59
Main drawback for me is length of this solution, it's not so clear and concise. But someone might actually prefer this. – Denis Malinovsky Jul 25 '14 at 16:56
Wouldn't this be an infinity value of a different type? – szablica Oct 31 '14 at 21:26
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Let's see: `Decimal('Infinity') == float('inf')` returns `True`, so it's pretty much the same. – Denis Malinovsky Nov 01 '14 at 18:17
His question is if wouldn't it be of a different type and the answer is yes. Should've checked `Decimal('Infinity') is float('inf')` and that's a `False` – Afzal S.H. Jun 22 '15 at 07:47
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@afzal_SH `float('inf') is float('inf')` returns `False` too – nemesisdesign Jun 27 '15 at 16:24
6

infinity is different even from itself, so your comment didn't make much sense to me, IMHO – nemesisdesign Jun 29 '15 at 13:20
1

@nemesisdesign Not true. `Inf == Inf` in standard float arithmetic. Maybe you are thinking of `NaN != NaN`? – a06e Mar 17 '17 at 13:45
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@becko, in python the `==` operator and the `is` operator mean two different things. Try to run in the python REPL the following code: `float('inf') is float('inf')` and `float('inf') == float('inf')` – nemesisdesign Mar 21 '17 at 14:36
10

`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: https://stackoverflow.com/questions/2988017/string-comparison-in-python-is-vs – Manoel Vilela Sep 01 '17 at 10:51

Antony Hatchkins · Answer 7 · 2015-07-09T04:45:53.610

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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()

edited Jul 09 '15 at 04:45

answered Nov 08 '14 at 10:07

Antony Hatchkins

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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` – Ali Rasim Kocal Jan 08 '15 at 14:41
6

But you don't have to use this. – Joost Aug 18 '15 at 12:26

score 12 · Answer 8 · edited Nov 08 '19 at 14:53

12

Also if you use SymPy you can use sympy.oo

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

etc.

edited Nov 08 '19 at 14:53

Georgy

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answered Aug 05 '19 at 15:54

USERNAME GOES HERE

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Erick Mwazonga · Answer 9 · 2023-05-14T11:18:41.883

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

score 2 · Answer 10 · answered Feb 17 '22 at 17:37

2

For Positive Infinity

pos_inf_val = float("infinity")

For Negative Infinity

neg_inf_val = float("-infinity")

answered Feb 17 '22 at 17:37

Omar

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score 0 · Answer 11 · answered Feb 22 '22 at 10:56

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

score 0 · Answer 12 · answered Mar 14 '22 at 13:28

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")

answered Mar 14 '22 at 13:28

Zgpeace

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score 0 · Answer 13 · answered Feb 11 '23 at 09:10

0

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.

answered Feb 11 '23 at 09:10

Pythoneer

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How can I represent an infinite number in Python?

13 Answers13

Infinity

1. Using `float('inf')` and `float('-inf)`

2. Using Python’s math module

3. Integer `maxsize`

4. Using Python’s decimal module

5. Using Numpy Library

Output:

Linked

Related

How can I represent an infinite number in Python?

13 Answers13

Infinity

1. Using float('inf') and float('-inf)

2. Using Python’s math module

3. Integer maxsize

4. Using Python’s decimal module

5. Using Numpy Library

Output:

Linked

Related

1. Using `float('inf')` and `float('-inf)`

3. Integer `maxsize`