Comparison operators

Comparison operators are used to compare values using mathematical logic and return a single Boolean value of either True or False. We will see later that they are important for counting, extracting and modifying data. For example, counting the number of students with GPA higher than a given threshold requires a comparison, for each student, of their GPA to the threshold.

In the cell below, Python compares two integers (is 5 strictly smaller than 7?) and returns the Boolean that reflects the comparison.

5<7

True

In the expression above, Python followed mathematical logic and declared the comparison to be true.

Below is a table of comparison operators.

Operator	What it means
==	Equal
!=	Not equal
<	Less than
<=	Less or equal
>	Greater than
>=	Greater or equal

To better understand how these operators work, we illustrate their use in the cell below where we compare two real numbers.

x = 1.5
y = 0.8

print("x == y:", x == y)
print("x != y:", x != y)
print("x < y:", x < y)
print("x <= y:", x <= y)
print("x > y:", x > y)
print("x >= y:", x >= y)

x == y: False
x != y: True
x < y: False
x <= y: False
x > y: True
x >= y: True

We showed examples of comparisons of integers and floats, but strings can also be used with comparison operators.

a='Dan'
b='Mike'

print("a == b:", a == b)
print("a != b:", a != b)
print("a < b:", a < b)
print("a <= b:", a <= b)
print("a > b:", a > b)
print("a >= b:", a >= b)

a == b: False
a != b: True
a < b: True
a <= b: True
a > b: False
a >= b: False

As you can see, Python compared the two strings and found them different, but is also able to use inequality operators to compare them. The order is determined lexicographically using the ASCII values of the characters.

Letter case is important for comparisons:

'Dan'=='dan'

False

Logical (boolean) operators

Python’s logical operators perform Boolean arithmetic on one or two inputs and return either True or False. The table below shows three logical operators.

Operator	What it means	Examples (that return True)
and	True if both are true	(7>5) and (1.2!=1.3)
or	True if at least one is true	(7<5) or (1.2!=1.3)
not	True if input is false	not(7==5)

print((7>5) and (1.2!=1.3))
print((7>5) & (1.2!=1.3))

print((7<5) or (1.2!=1.3))
print((7<5) | (1.2!=1.3))

True
True
True
True

Note: You will see in some code examples here and elsewhere the logic operators and and or replaced by something called bitwise operators: & used instead of and and | instead of or. Note that, even if they give the same results when applied to boolean data types (as in the examples above), they have different meanings for other data types. We will use mostly and and or in this textbook.

Finally, an expression can contain multiple comparisons, and all comparisons must hold in order for the whole expression to be True. You can see a couple of examples below. In the first, Python evaluates first the expression 5-2 (equal to 3), then evaluates 1.2 <= 1.8 and 1.8 < 3 (both True), and finally use the boolean operator and to evaluate the full expression.

1.2 <= 1.8 < 5-2

True

'Dan' != 'Mike' == 'Nike'

False

Truth tables

An easy way to summarize the outcome of logic operators are truth tables, and we show them below for and and or. Note that we used them in the multiple comparisons above. They are useful for algorithmic thinking in programming. For simplicity we summarize them in a single table.

a	b	a and b	a or b
True	True	True	True
True	False	False	True
False	True	False	True
False	False	False	False