Relations

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We can hardly think for a minute without asking a question. All day long we think in terms of questions. What are we doing when we ask questions? How can they be that intrical to our view of the world? [ Two questions already. ]

Anatomy of a Question

What is the underlying assumption of a question?

Connecting Information

What ingredients are needed to make chili?
Who was in House of Wax (1953)?
What is the speed limit on Route 3?
What is Camila’s social security number?
What ice cream flavors does Kevin like?
What is $32^\circ F$ in Celsius?
Could you provide a list of good mystery books and their authors?
Did you pass Chemistry?
How high is Mt. Everest?
Who are Timothy’s nieces?
What are the Post Office’s hours?

$\blacktriangleright$ We understand our world through connections between things.

We might view this as characteristics or attributes of something.

Mt Everest is $29,029 ft$ tall.

We might experience this as an if-then statement.

If you are driving on Route 3, then do not go over 35 mph.

We might experience this as cause and effect.

The Post Office is closed, because it is 9:00pm.

All of our questions assume the same structure.

Questions assume there are two sets or collections of things and that the items from each set are connected or associated with items in the other collection.

Movies and Actors
There is a set or collection of movies and a set or collection of actors. A movie is associated with an actor if the actor appeared in the movie.

SSN
There is a set of 9-digit numbers and a collection of U.S. citizens. A number is connected to a person if the person was issued the number as their social security number.

Hours of Operation
There is a collection of Post Offices and a collection of times. A time is connected to a Post Office if the Post Office is open for buiness during those hours.

There is certainly a pragmatic side to questions.

But, also, questions express our curiosity into the structure of how collections of things are connected. Mathematics is one way in which we describe such structures. Our mathematical word for these connected collections is a relation.

This section explores relations and how we communicate about them.

Learning Outcomes

In this section, students will

view a relation as a structured package.
encode relation pairings as written ordered pairs.
decipher written ordered pairs into relation pairings.
trace connections back-and-forth between sets.

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more examples can be found by following this link
More Examples of Relations