List comprehensions are used for creating lists from existing lists and other iterable structures. List comprehensions typically follow formatting similar to set-builder notation in discrete mathematics.

Consider the following illustrative Python3 example for generating a list of squares:

>>> sq = []
>>> for i in range(10):
...  sq.append(i**2)
... 
>>> sq
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

The same could be achieved in the following list comprehension:

>>> [x**2 for x in range(10)]
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

The following defines the set of all squares, n² such that n is an integer and n is in the range 0..9: {n² | n ∈ Z ∧ 0 ≤ n ≤ 9 }.