Integers

2. Basic Types: Numbers

Integers

Now that we have shown that and are equal to and in Python, it might come as no surprise that the $\color{#4271ae} {\mathtt{\text{bool}}}$ type is actually a subtype of the type that includes all the integers; $\color{#4271ae} {\mathtt{\text{int}}}$ . Similar to $\color{#4271ae} {\mathtt{\text{bool}}}$ being a shorthand for boolean, $\color{#4271ae} {\mathtt{\text{int}}}$ is a shorthand for integer.

Integer defintionAn integer is defined as a number that can be written without a fractional component. In computer science, integer refers to a data type that describes some range of mathematical integers.

Like in mathematics, integers in Python support a variety of mathematical operations. Their use is very similar to how you would use them on a calculator, barring some exceptions.

Operator definitions

The most common mathematical operators supported by $\color{#4271ae} {\mathtt{\text{int}}}$ :

Operator	Name	Usage	Returns
$\mathtt{\text{+}}$	Addition	$\mathtt{\text{x}}$ $\mathtt{\text{y}}$	The sum of $\mathtt{\text{x}}$ and $\mathtt{\text{y}}$ .
$\mathtt{\text{-}}$	Subtraction	$\mathtt{\text{x}}$ $\mathtt{\text{y}}$	$\mathtt{\text{x}}$ subtracted by $\mathtt{\text{y}}$ .
$\mathtt{\text{*}}$	Multiplication	$\mathtt{\text{x}}$ $\mathtt{\text{y}}$	$\mathtt{\text{x}}$ multiplied by $\mathtt{\text{y}}$ .
$\mathtt{\text{/}}$	Division	$\mathtt{\text{x}}$ $\mathtt{\text{y}}$	$\mathtt{\text{x}}$ divided by $\mathtt{\text{y}}$ .
$\mathtt{\text{**}}$	Exponentiation	$\mathtt{\text{x}}$ $\mathtt{\text{y}}$	$\mathtt{\text{x}}$ to the power of $\mathtt{\text{y}}$

Less common, but still useful operators supported by $\color{#4271ae} {\mathtt{\text{int}}}$ :

Operator	Name	Usage	Returns
$\mathtt{\text{%}}$	Modulo or Modulus	$\mathtt{\text{x}}$ $\mathtt{\text{y}}$	The remainder of $\mathtt{\text{x}}$ divided by $\mathtt{\text{y}}$ .
$\mathtt{\text{//}}$	Floor Division or Integer Division	$\mathtt{\text{x}}$ $\mathtt{\text{y}}$	The result of $\mathtt{\text{x}}$ divided by $\mathtt{\text{y}}$ rounded down (floored) to $\mathtt{\text{int}}$ .

Let's take a look at the operators in action, most of them should be familiar.

Operator examplesSimple integer addition:

>>> 10 + 10

>>> 10 + 10 + 10

Subtraction

Integer subtraction, double subtraction results in addition:

>>> 36 - 12

>>> 36 - -12

Multiplication

Multiplication:

>>> 2 * 4

Division

Normal division returns a value with a fractional component while integer division returns a value that is rounded down to the nearest integer (floored).

>>> 8 / 5

1.6

>>> 8 // 5

We can use the modulo operator to obtain the remainder of a division:

>>> 8 % 4

>>> 8 % 3

When using modulo with a denominator greater than the numerator, the numerator is returned.

>>> 8 % 9

Exponentiation

We can use $\color{#3e999f} {\mathtt{\text{**}}}$ to raise numbers to the power of something, it's equivalent to $\mathtt{\text{^}}$ on your calculator.

>>> 2 ** 4

Just like we used parentheses in boolean expressions we can use them here to modify the order of evaluation.

Parentheses examplesWe can use parentheses to subvert operator precedence:

>>> 4 + 4 * 4

>>> (4 + 4) * 4

Even when parentheses are not necessary it might be useful to add them anyway to make your code more explicit.

>>> 36 - (-12)

Booleans in Python inherit all functionality from integers, so it's possible to perform calculations with $\color{#F5871F} {\mathtt{\text{True}}}$ and $\color{#F5871F} {\mathtt{\text{False}}}$ . They will simply evaluate to $\color{#F5871F} {\mathtt{\text{1}}}$ and $\color{#F5871F} {\mathtt{\text{0}}}$ within mathematical expressions.

As a subtype of $\color{#4271ae} {\mathtt{\text{int}}}$ , $\color{#4271ae} {\mathtt{\text{bool}}}$ inherits the same functionality:

>>> True + False

>>> True * 3 / True

3.0