The theoretical domain for integers in python is negative infinity to infinity. In practice, integer values are limited by the amount of available memory.

In Python 2, there was a distinction between int, numbers that fit in a 32 or 64 bit C long, and long, numbers limited by available memory. Python 3 unified the two types into just int, more info in PEP 237.

int creation using integer literals

Integer Literals

Integer objects can be created using using integer literals. Unadorned numbers without decimals are integer literals:

>>> 1234567890           # Unadorned numbers are integer literals
1234567890
>>> type(1234567890)
<class 'int'>

Numeric literals do not contain a sign, however creating negative integer objects is possible by prefixing with a unary - (minus) operator with no space before the literal:

>>> -1234567890
-1234567890
>>> type(-1234567890)
<class 'int'>

Likewise, positive integer objects can be created by prefixing a unary + (plus) operator with no space before the digits. Usually + is ommited:

>>> +1234
1234

Binary (base 2, prefix: 0b or 0B), octal (base 8, prefix: 0o or 0O), and hexadecimal (base 16, prefix: 0x or 0X) integers can also be created using integer literals:

>>> 0b1, 0b10, 0b11
(1, 2, 3)
>>> 0o1, 0o10, 0o11
(1, 8, 9)
>>> 0x1, 0x10, 0x11
(1, 16, 17)

Note that leading 0's for non-zero integer literals are not allowed:

>>> 0     # Zero by itself is okay.
0
>>> 01    # Leading zero(s) cause SyntaxError.
  File "<stdin>", line 1
    01
     ^
SyntaxError: invalid token

The int constructor is another way to create integer objects.

class int(x=0)
class int(x, base=10)

Creating integer objects with integer literals is preferred when possible:

>>> a = 1         # Prefer integer literal when possible.
>>> type(a)
<class 'int'>
>>> b = int(1)    # Works but unnecessary.
>>> type(b)
<class 'int'>

However, the constructor allows for creating integer objects from other number types:

>>> a = 1.123
>>> type(a)
<class 'float'>
>>> print(a)
1.123
>>> b = int(1.123)
>>> type(b)
<class 'int'>
>>> print(b)
1

Using the int constructor for floating point numbers will truncate the number towards zero:

>>> int(-1.23)
-1
>>> int(1.23)
1

The built-in boolean constants are instances of the bool class, and are subclasses of the int class, making them a kind of numeric type:

>>> type(True)
<class 'bool'>
>>> issubclass(bool, int)
True

If that doesn't make sense to you, don't worry. For now just remember that calling the int constructor with boolean objects will return integer objects:

>>> int(True)
1
>>> int(False)
0

The int constructor will also make integer objects from strings:

>>> a = "10"
>>> type(a)
<class 'str'>
>>> b = int("10")
>>> type(b)
<class 'int'>

Strings for the int constructor must represent an integer literal:

The second parameter of the int constructor is to specify a base (default: 10). Valid bases are 0 and 2-36.

If an explicit base is provided the first argument must be a string.

>>> int("111", 2)
7
>>> int(111, 2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: int() can't convert non-string with explicit base

The string used for the int constructor with an explicit base must be a valid integer literal for that base:

>>> int('11', 2)
3
>>> int('12', 2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: invalid literal for int() with base 2: '12'

Both prefixed and non-prefixed strings of integer literals can be used, however, if used, the prefix must match the provided base.

>>> int('1101', 2)
13
>>> int('0b1101', 2)
13
>>> int('0x1101', 2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: invalid literal for int() with base 2: '0x1101'

If a prefixed string and base 0 is used, the created integer object will use the base specified by the prefix. If no prefix is used, then the base is assumed 10

>>> int('100', 0)
100
>>> int('0b100', 0)
4
>>> int('0o100', 0)
64

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