Comparisons

2. Basic Types: Numbers

Comparisons

In addition to operators for standard arithmetic, Python also provides operators meant for comparisions. Each of these operators also has their mathematical equivalent. In mathematics we use #=# to test for equality, in Python the #\color{#3e999f} {\mathtt{\text{=}}}# is reserved for variable assignment, so #\color{#3e999f} {\mathtt{\text{==}}}# is used for equality instead. All comparison operators are used to compare two values or objects.

Operator definition

Operator	Name	Equivalent	Expression	Returns
#\mathtt{\text{==}}#	Equal	#x = y#	#\mathtt{\text{x}}# #\mathtt{\text{==}}# #\mathtt{\text{y}}#	#\color{#F5871F} { \mathtt{\text{True}} }# if #\mathtt{\text{x}}# is equal to #\mathtt{\text{y}}#, otherwise #\color{#F5871F} {\mathtt{\text{False}}}#.
#\mathtt{\text{!=}}#	Not equal	#x \neq y#	#\mathtt{\text{x}}# #\mathtt{\text{!=}}# #\mathtt{\text{y}}#	#\color{#F5871F} { \mathtt{\text{True}} }# if #\mathtt{\text{x}}# is not equal to #\mathtt{\text{y}}#, otherwise #\color{#F5871F} {\mathtt{\text{False}}}#.
#\mathtt{\text{>}}#	Greater than	#x \gt y#	#\mathtt{\text{x}}# #\mathtt{\text{>}}# #\mathtt{\text{y}}#	#\color{#F5871F} { \mathtt{\text{True}} }# if #\mathtt{\text{x}}# is greater than #\mathtt{\text{y}}#, otherwise #\color{#F5871F} {\mathtt{\text{False}}}#.
#\mathtt{\text{<}}#	Less than	#x \lt y#	#\mathtt{\text{x}}# #\mathtt{\text{<}}# #\mathtt{\text{y}}#	#\color{#F5871F} { \mathtt{\text{True}} }# if #\mathtt{\text{x}}# is less than #\mathtt{\text{y}}#, otherwise #\color{#F5871F} {\mathtt{\text{False}}}#.
#\mathtt{\text{>=}}#	Greater than or equal to	#x \geq y#	#\mathtt{\text{x}}# #\mathtt{\text{>=}}# #\mathtt{\text{y}}#	#\color{#F5871F} { \mathtt{\text{True}} }# if #\mathtt{\text{x}}# is greater than or equal to #\mathtt{\text{y}}#, otherwise #\color{#F5871F} {\mathtt{\text{False}}}#.
#\mathtt{\text{<=}}#	Less than or equal to	#x \leq y#	#\mathtt{\text{x}}# #\mathtt{\text{<=}}# #\mathtt{\text{y}}#	#\color{#F5871F} { \mathtt{\text{True}} }# if #\mathtt{\text{x}}# is less than or equal to #\mathtt{\text{y}}#, otherwise #\color{#F5871F} {\mathtt{\text{False}}}#.

The comparison expressions return either #\color{#F5871F} { \mathtt{\text{True}} }# or #\color{#F5871F} { \mathtt{\text{False}} }# when the expression is true or untrue. Let's take a look at some examples.

Comparison examplesSimply test the value of a variable:

>>> var = 1 + 1
>>> var == 1

False

>>> var == 2

True

But, we can use #\color{#3e999f} {\mathtt{\text{!=}}}# to check if #\mathtt{\text{var}}# is not equal to #\color{#F5871F} {\mathtt{\text{1}}}#. This is the same as testing the negation of equality.

>>> var != 1

True

>>> not var == 1

True

It is important to realize that #\color{#3e999f} {\mathtt{\text{==}}}# does not test for type equality, which means that objects of type #\color{#4271ae} {\mathtt{\text{int}}}# and #\color{#4271ae} {\mathtt{\text{float}}}# representing the same value are equal.

>>> 3 == 3.0

True

However, it is crucial to note that different expressions containing different combinations of #\color{#4271ae} {\mathtt{\text{int}}}# or #\color{#4271ae} {\mathtt{\text{float}}}# do not necessarily return the same value, even if they should. This is a common occurence in any programming language, and the result of the so called floating point error, which can result in unexpected behaviour.

>>> 1 + 2 == (0.1 + 0.2) * 10

False

>>> 1 + 2

>>> (0.1 + 0.2) * 10

3.0000000000000004

Floating point errors are the result of underlying floating point formats at the lowest level of computer memory only being able to achieve limited precision.

Greater than

We can use the #\color{#3e999f} {\mathtt{\text{>}}}# to test whether expressions result in greater values than other expressions.

>>> var = 10
>>> var > 0

True

Similarly, we can use #\color{#3e999f} {\mathtt{\text{>=}}}# to test whether expressions result in greater or equal values than other expressions.

>>> 10 > 10

False

>>> 10 >= 10

True

Again, by mixing boolean operators and comparison operators we can achieve the same behaviour.

>>> var = 10
>>> var > 10 or var == 10

True

It is very common to use these operators to test whether an expression or value is contained within an inclusive or exclusive range, for example checking if #\mathtt{\text{n}} \in [1, 100)#.

>>> n = 10
>>> 100 > n >= 1

True

This is a shorthand for this:

>>> 100 > n and n >= 1

True

Less than

In contrast, we can use the #\color{#3e999f} {\mathtt{\text{<}}}# to test whether expressions result in lesser values than other expressions. Similarly, #\color{#3e999f} {\mathtt{\text{<=}}}# can be used to test whether expressions result in lesser or equal values than other expressions.

>>> 1 < 2

True

>>> 2 < 2

False

>>> 2 <= 2

True

Like the greater than symbols, #\color{#3e999f} {\mathtt{\text{<}}}# and #\color{#3e999f} {\mathtt{\text{<=}}}# can also be used to test whether values or expressions are within a given range.