Python Language Math Module Infinity and NaN ("not a number")
Example
In all versions of Python, we can represent infinity and NaN ("not a number") as follows:
pos_inf = float('inf') # positive infinity
neg_inf = float('-inf') # negative infinity
not_a_num = float('nan') # NaN ("not a number")
In Python 3.5 and higher, we can also use the defined constants math.inf and math.nan:
Python 3.x3.5
pos_inf = math.inf
neg_inf = -math.inf
not_a_num = math.nan
The string representations display as inf and -inf and nan:
pos_inf, neg_inf, not_a_num
# Out: (inf, -inf, nan)
We can test for either positive or negative infinity with the isinf method:
math.isinf(pos_inf)
# Out: True
math.isinf(neg_inf)
# Out: True
We can test specifically for positive infinity or for negative infinity by direct comparison:
pos_inf == float('inf') # or == math.inf in Python 3.5+
# Out: True
neg_inf == float('-inf') # or == -math.inf in Python 3.5+
# Out: True
neg_inf == pos_inf
# Out: False
Python 3.2 and higher also allows checking for finiteness:
Python 3.x3.2
math.isfinite(pos_inf)
# Out: False
math.isfinite(0.0)
# Out: True
Comparison operators work as expected for positive and negative infinity:
import sys
sys.float_info.max
# Out: 1.7976931348623157e+308 (this is system-dependent)
pos_inf > sys.float_info.max
# Out: True
neg_inf < -sys.float_info.max
# Out: True
But if an arithmetic expression produces a value larger than the maximum that can be represented as a float, it will become infinity:
pos_inf == sys.float_info.max * 1.0000001
# Out: True
neg_inf == -sys.float_info.max * 1.0000001
# Out: True
However division by zero does not give a result of infinity (or negative infinity where appropriate), rather it raises a ZeroDivisionError exception.
try:
x = 1.0 / 0.0
print(x)
except ZeroDivisionError:
print("Division by zero")
# Out: Division by zero
Arithmetic operations on infinity just give infinite results, or sometimes NaN:
-5.0 * pos_inf == neg_inf
# Out: True
-5.0 * neg_inf == pos_inf
# Out: True
pos_inf * neg_inf == neg_inf
# Out: True
0.0 * pos_inf
# Out: nan
0.0 * neg_inf
# Out: nan
pos_inf / pos_inf
# Out: nan
NaN is never equal to anything, not even itself. We can test for it is with the isnan method:
not_a_num == not_a_num
# Out: False
math.isnan(not_a_num)
Out: True
NaN always compares as "not equal", but never less than or greater than:
not_a_num != 5.0 # or any random value
# Out: True
not_a_num > 5.0 or not_a_num < 5.0 or not_a_num == 5.0
# Out: False
Arithmetic operations on NaN always give NaN. This includes multiplication by -1: there is no "negative NaN".
5.0 * not_a_num
# Out: nan
float('-nan')
# Out: nan
Python 3.x3.5
-math.nan
# Out: nan
There is one subtle difference between the old float versions of NaN and infinity and the Python 3.5+ math library constants:
Python 3.x3.5
math.inf is math.inf, math.nan is math.nan
# Out: (True, True)
float('inf') is float('inf'), float('nan') is float('nan')
# Out: (False, False)
