Assigning a variable NaN in python without numpy

Yes — use math.nan.

>>> from math import nan
>>> print(nan)
nan
>>> print(nan + 2)
nan
>>> nan == nan
False
>>> import math
>>> math.isnan(nan)
True

Before Python 3.5, one could use float("nan") (case insensitive).

Note that checking to see if two things that are NaN are equal to one another will always return false. This is in part because two things that are “not a number” cannot (strictly speaking) be said to be equal to one another — see What is the rationale for all comparisons returning false for IEEE754 NaN values? for more details and information.

Instead, use math.isnan(...) if you need to determine if a value is NaN or not.

Furthermore, the exact semantics of the == operation on NaN value may cause subtle issues when trying to store NaN inside container types such as list or dict (or when using custom container types). See Checking for NaN presence in a container for more details.

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You can also construct NaN numbers using Python’s decimal module:

>>> from decimal import Decimal
>>> b = Decimal('nan')
>>> print(b)
NaN
>>> print(repr(b))
Decimal('NaN')
>>>
>>> Decimal(float('nan'))
Decimal('NaN')
>>> 
>>> import math
>>> math.isnan(b)
True

math.isnan(...) will also work with Decimal objects.

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However, you cannot construct NaN numbers in Python’s fractions module:

>>> from fractions import Fraction
>>> Fraction('nan')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "C:Python35libfractions.py", line 146, in __new__
    numerator)
ValueError: Invalid literal for Fraction: 'nan'
>>>
>>> Fraction(float('nan'))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "C:Python35libfractions.py", line 130, in __new__
    value = Fraction.from_float(numerator)
  File "C:Python35libfractions.py", line 214, in from_float
    raise ValueError("Cannot convert %r to %s." % (f, cls.__name__))
ValueError: Cannot convert nan to Fraction.

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Incidentally, you can also do float('Inf'), Decimal('Inf'), or math.inf (3.5+) to assign infinite numbers. (And also see math.isinf(...))

However doing Fraction('Inf') or Fraction(float('inf')) isn’t permitted and will throw an exception, just like NaN.

If you want a quick and easy way to check if a number is neither NaN nor infinite, you can use math.isfinite(...) as of Python 3.2+.

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If you want to do similar checks with complex numbers, the cmath module contains a similar set of functions and constants as the math module:

• cmath.isnan(...)
• cmath.isinf(...)
• cmath.isfinite(...) (Python 3.2+)
• cmath.nan (Python 3.6+; equivalent to complex(float('nan'), 0.0))
• cmath.nanj (Python 3.6+; equivalent to complex(0.0, float('nan')))
• cmath.inf (Python 3.6+; equivalent to complex(float('inf'), 0.0))
• cmath.infj (Python 3.6+; equivalent to complex(0.0, float('inf')))