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Querying Relational Databases

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Set Theory and Relational Databases

4:36 with Andrew Chalkley and Kevin Nahm

Now that we understand a little bit about what Relational Databases are and why we structure them the way we do, let’s take a higher-level look at how to think about data.

Introduction to Set Theory

Set Theory was founded in 1874, and is a relatively new mathematical discipline, as compared to Algebra or Calculus.
For more history and info about the topic, check out the Wikipedia page on Set Theory

This link takes a look at Set Operations in SQL, but we’ll be covering this more in a later stage.

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    Now that we understand a little bit about what relational databases are and 0:00
    why we structure them in the way that we do. 0:04
    Let's take a high level look at how to think about data. 0:07
    You can think of a database table as a set of data stored to a disk. 0:11
    You can add and remove dates to the set and you can update it. 0:15
    When you query a table you get the whole set or even a subset of data back. 0:20
    This is known as a result set. 0:26
    You may have notice me saying the word set a lot. 0:29
    A set means a grouping of similar things and 0:31
    they are the foundation of performing useful queries in relational databases. 0:34
    Let's take a look at a few examples of some simple sets. 0:39
    Remember, a set means a grouping of similar things together. 0:44
    You could have a set of things you can wear. 0:48
    Shirts, shoes, socks, coats, or you could have a more specific set of shirts. 0:50
    T-shirt, dress-shirts, sweaters. 0:56
    Items like shoes and socks belong in the first set but not the second set. 1:00
    You can wear socks and shoes but they aren't types of a shirt. 1:05
    Or you could have a set of fruits, apples, bananas, strawberries, pears. 1:09
    Or sets of apples, granny smith, fugue, red delicious. 1:14
    In this example, the definition of the second set, apples, 1:18
    excludes items from the more inclusive set of all fruits. 1:22
    You can also depicts sets conceptually as graphs called the Venn diagrams. 1:28
    These graphs help us show whereas one set might overlap with another or 1:33
    why one set is distinct from other sets. 1:37
    Let's say we have a group of people who like certain types of fruits and 1:41
    we want to show who likes what. 1:45
    We can depict this with Venn diagrams. 1:48
    Here we have two small sets. 1:51
    The set of people who like apples and the set of people who like bananas. 1:53
    The people who like apples are John, Stacy, Indira and Bob. 1:58
    And the people who like bananas are Indira, Bob and Dante. 2:05
    Now let's look at a common element for both sets. 2:10
    In this case, the elements are people. 2:14
    As we overlay the two sets you can see that both Bob and 2:17
    Indira are the two people who like both apples and bananas. 2:22
    This area in the middle is called the intersection between two sets. 2:26
    The entirety of both circles combined, 2:31
    in this case all people who like apples or bananas, is called the union. 2:34
    Finally, what if we want to just find the people who like one fruit or 2:41
    the other but not both. 2:46
    This is called an except, all people who like apples, and 2:48
    all people who like bananas except the people who like both. 2:52
    When we perform an intersection, union or 2:58
    except on sets of data, these are known as set operations. 3:01
    Remember, tables and the results from queries a called data sets. 3:06
    When you write a query for a report or 3:10
    dynamic application, you're actually working with datasets. 3:12
    That can have set operations performed on them. 3:17
    Remember that a set is a collection of similar things, a data set 3:20
    is nothing more than a collection of rows with the same column definitions. 3:25
    A table is a data set that is stored physically on a disk. 3:30
    Let's take a look at our Venn diagram example again, but 3:35
    this time let's use data. 3:38
    Here we see two small tables, our group of people who like apples is in 3:41
    one table and then the group of the other people who like bananas in another. 3:46
    Let's analyze that data for the people who like both apples and bananas. 3:52
    This is the intersection from our Venn diagram a minute ago. 3:57
    Now, let's see all people regardless of which fruit they like. 4:01
    This is the union from our Venn diagram. 4:06
    And now let's look for just people that like one fruit or the other, but not both. 4:08
    This is the except example from a minute ago. 4:14
    This normalization process helps databases perform set operations of intersection, 4:17
    union, and except in fast and efficient ways. 4:23
    As we get deeper into this course, we'll study this in more detail. 4:27
    Keep the image of a Venn diagram in your mind to help you visualize the concepts. 4:31

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