Integers

2. Basic Types: Numbers

Integers

Now that we have shown that #\mathtt{\text{True}}# and #\mathtt{\text{False}}# are equal to #\mathtt{\text{1}}# and #\mathtt{\text{0}}# 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{+}}# #\mathtt{\text{y}}#	The sum of #\mathtt{\text{x}}# and #\mathtt{\text{y}}#.
#\mathtt{\text{-}}#	Subtraction	#\mathtt{\text{x}}# #\mathtt{\text{-}}# #\mathtt{\text{y}}#	#\mathtt{\text{x}}# subtracted by #\mathtt{\text{y}}#.
#\mathtt{\text{*}}#	Multiplication	#\mathtt{\text{x}}# #\mathtt{\text{*}}# #\mathtt{\text{y}}#	#\mathtt{\text{x}}# multiplied by #\mathtt{\text{y}}#.
#\mathtt{\text{/}}#	Division	#\mathtt{\text{x}}# #\mathtt{\text{/}}# #\mathtt{\text{y}}#	#\mathtt{\text{x}}# divided by #\mathtt{\text{y}}#.
#\mathtt{\text{**}}#	Exponentiation	#\mathtt{\text{x}}# #\mathtt{\text{**}}# #\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{%}}# #\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{//}}# #\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.

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

>>> True + False

>>> True * 3 / True

3.0