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We'll finish this section by looking at the last 
of Python's built-in data structures – sets. 

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A set is an unordered collection 
with no duplicate entries. Python 

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sets work the same way as they do in set theory.
If you don't know about set theory, don't worry. 

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We're not going to go into the 
mathematics of set theory here. 

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Set theory is an interesting, and 
important, branch of mathematics. 

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But we're going to use Python sets to 
solve some common programming problems. 

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I won't be getting all 
mathematical in these videos. 

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If you are familiar with set theory, then 
you'll find that Python sets behave exactly 

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how you'd expect. You can perform 
all the usual set operations on them. 

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We'll be looking at those operations in a 
non-mathematical context, but you'll have 

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no problem applying them to mathematical uses 
of sets, if that's something you need to do. 

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I'll be using slides to explain things 
like set union and intersection. 

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Fast forward those parts of the videos, if 
you're already familiar with those operations. 

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The keys of a dictionary are very similar to 
a set. The main difference, since Python 3.7, 

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is that dictionary keys are ordered.
Sets have no ordering. 

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That's an important point, and explains 
why you can't do certain things with sets. 

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For example, there's no way to 
access individual elements of a set. 

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We'll see that sets are unordered, when we 
iterate over some sets in the next video. 

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Before that, I'll introduce 
the basic set operations. 

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Here, we've got two sets. They 
represent a collection of farm animals, 

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on the left, and wild animals, on the right. 

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The sets are over-simplified, to 
keep them easier to understand. 

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You'd struggle to find wild cows these days, but 
there are wild sheep in many parts of the world. 

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We're keeping things simple: sheep 
is only in the farm_animals set. 

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When we represent sets with circles, like these, 
it's easier to see that they are unordered. 

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A set is just a collection of items. Our 
animals could wander about inside their circles, 

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but the set would still contain the same items. 

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The most common operation we can perform 
on a set, is to test for membership. 

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Looking at the farm_animals set, we can 
see that cow is a member of farm_animals. 

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hen, sheep, goat, and horse are also 
members of the farm_animals set. 

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In Python, we test for 
membership using the in keyword. 

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We've seen that with lists, tuples and 
dictionaries, and it works the same with sets. 

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tiger is a member of the wild_animals set, so the 
condition 'tiger' in wild_animals will be True. 

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Testing if something is in a set can make our code 
more efficient. It's also a good way to fix a bug 

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that we had, in our very early menu programs.
We'll have a look at that, in the next video. 

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The union of two or more sets, is the set 
of all items that exist in all the sets. 

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Here, we have the union of 
the farm_animals and wild_animals sets. 

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In Python, the union of these two sets is written:
farm_animals.union(wild_animals) 

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or
farm_animals | wild_animals 

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One important point to notice, looking at our 
union set, is that items only appear once. 

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The elements of a set are unique. 
That's part of the definition of a set. 

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goat and horse appear in both sets, but 
they only appear once in the union set. 

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It doesn't make sense for something 
to be in a set more than once. 

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That property of sets – that the 
items are unique (or distinct, 

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in mathematical terms) – 
can be useful in our code. 

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Converting a list to a set, for example, will 
automatically remove any duplicate values. 

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Once again, we'll see some 
examples of this, later. 

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At the moment, we're just learning the 
basic terminology that applies to sets. 

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The intersection of two or more sets, is 
the set of items that appear in all sets. 

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That's quite easy to remember – it's the 
items that appear in the area where our 

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circles intersect. We can see that horse and goat 
are in both sets, and appear in the orange area. 

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If we had a third set, of animals 
that can be ridden, for example, 

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then horse would probably be the only 
animal in the intersection of all 3 sets. 

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It may be possible to ride a goat, 
but it's certainly not very common . 

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The Python code representing 
this intersection would be: 

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farm_animals.intersection(wild_animals) 

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or
farm_animals & wild_animals 

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You can also subtract one set from another. Here, 
we've subtracted wild_animals from farm_animals. 

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That leaves cow, sheep and hen. Any 
items from wild_animals are removed, 

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when we subtract the two sets. 

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In Python, we'd write that as either
farm_animals - wild_animals 

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or
farm_animals.difference(wild_animals) 

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Set theory also defines a symmetric difference. 

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The symmetric difference is the set of items 
that are in one set or the other, but not both. 

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In this example, the symmetric difference 
doesn't include goat and horse. 

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All the animals in the orange areas are 
included in the symmetric difference. 

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It's the opposite of the 
intersection of 2 or more sets. 

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In Python, we'd write that as:
farm_animals.symmetric_difference(wild_animals) 

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or
farm_animals ^ wild_animals 

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One set can also be a subset of another set.
We use the normal comparison 

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operators; <, <=, > and >=, to check for subsets.
But that's enough slides, and theory, for now. 

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We'll leave subsets and supersets until 
we've had some practice with using sets. 

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See you in the next video.