Integers

Python integers have an unlimited range, subject only to the available virtual memory. This means that it doesn't really matter how big a number you want to store is: as long as it can fit in your computer's memory, Python will take care of it. Integer numbers can be positive, negative, and 0 (zero). They support all the basic mathematical operations, as shown in the following example:

>>> a = 14
>>> b = 3
>>> a + b  # addition
17
>>> a - b  # subtraction
11
>>> a * b  # multiplication
42
>>> a / b  # true division
4.666666666666667
>>> a // b  # integer division
4
>>> a % b  # modulo operation (reminder of division)
2
>>> a ** b  # power operation
2744

The preceding code should be easy to understand. Just notice one important thing: Python has two division operators, one performs the so-called true division (/), which returns the quotient of the operands, and the other one, the so-called integer division (//), which returns the floored quotient of the operands. It might be worth noting that in Python 2 the division operator / behaves differently than in Python 3. See how that is different for positive and negative numbers:

>>> 7 / 4  # true division
1.75
>>> 7 // 4  # integer division, truncation returns 1
1
>>> -7 / 4  # true division again, result is opposite of previous
-1.75
>>> -7 // 4  # integer div., result not the opposite of previous
-2

This is an interesting example. If you were expecting a -1 on the last line, don't feel bad, it's just the way Python works. The result of an integer division in Python is always rounded towards minus infinity. If, instead of flooring, you want to truncate a number to an integer, you can use the built-in int function, as shown in the following example:

>>> int(1.75)
1
>>> int(-1.75)
-1

Notice that the truncation is done toward 0.

There is also an operator to calculate the remainder of a division. It's called a modulo operator, and it's represented by a percentage (%):

>>> 10 % 3  # remainder of the division 10 // 3
1
>>> 10 % 4  # remainder of the division 10 // 4
2

One nice feature introduced in Python 3.6 is the ability to add underscores within number literals (between digits or base specifiers, but not leading or trailing). The purpose is to help make some numbers more readable, like for example 1_000_000_000:

>>> n = 1_024
>>> n
1024
>>> hex_n = 0x_4_0_0  # 0x400 == 1024
>>> hex_n
1024