Sets

We will not spend long on sets as their use is somewhat limited, but they can come in very handy at times.

Unordered and unindexed
Items are immutable (unchangeable)
Set is mutable (changable)
Collection of distinct items

By unordered and unindexed we mean that the set does not have an order and therefore does not use indexing. You cannot access an item in a set by an index.

By items are immutable we mean that you cannot change an item in the set, this follows from it being unordered and unindexed. If you can't access an item, you definitely can't change it.

By set is mutable we mean that you can add and remove items from the set.

By collection of distinct items we mean that a set cannot contain duplicates.

You define a set as follows.

car_set = {"Audi", "Porsche", "Ford"}

Note that if you try and define a set with multiple items, it will only include one copy of each distinct item.

car_set = {"Audi", "Porsche", "Ford", "Audi"} # set is {"Audi", "Porsche", "Ford"}

1. Set Items

There are a few things we can do to a set involving items.

1.1 Is an Item in the Set?

The in keyword checks whether an item is in a given set and returns True or False.

"Audi" in car_set  # evaluates to True
"Skoda" in car_set # evaluates to False

Note that in can also be used on lists and tuples.

car_list = ["Audi", "Porsche", "Ford", "Audi"]
car_tuple = ("Audi", "Porsche", "Ford", "Audi")
"Audi" in car_list  # evaluates to True
"Audi" in car_tuple  # evaluates to True

1.2 Add an Item

You can add an item to a set by using the add() method.

car_set. add("Skoda") # set is {"Audi", "Porsche", "Ford", "Skoda"}

1.3 Remove an Item

You can remove an item in a set by using the remove() method.

car_set. remove("Ford") # set is {"Audi", "Porsche", "Skoda"}

2. Looping Through a Set

Just like lists and tuples, you can loop through a set.

car_set = {"Audi", "Porsche", "Ford"}
for car in car_set:
  print(car)

# prints...
# Audi
# Porsche
# Ford

3. Joining Sets

You can join sets using either the union() or intersection() methods.

For a mathematician, this is a very loose definition, but basically the union() method will include all the items that are in both sets, but not any duplicates.

a = {1,2,3}
b = {1,4,5,6}
c = a.union(b) # c now contains {1,2,3,4,5,6}

The intersection includes only the items that appear in both sets.

a = {1,2,3}
b = {1,4,5,6}
c = a.intersection(b) # c now contains {1}

4. Set Methods

There are a number of set methods that you can use, we have seen two in add() and remove(). We will not look at these in detail in this course.

You can find a full list here Python Set Methods - W3schools.

I suggest you use these when you are studying sets in computational mathematics.

=== TASK ===

Copy and paste the following into a new Python file to get started.

def items_in_both(a,b):
    pass

if __name__ == "__main__":
    # main
    # use this code to help check the function
    a = {1,2,3}
    b = {1,4,5,6}
    print(items_in_both(a,b))    # prints {1}

Update the function items_in_both() so that it returns the set that contains only the items that appear in both sets.

References

Python Sets - W3schools

Programming in Python