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?
- 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, and questions are how
we organize these connections.
We might view a connection as characteristics or attributes of something.
- Mt Everest is \(29,029 ft\) tall.
We might experience a connection as an if-then statement.
- If you are driving on Route 3, then do not go over 35 mph.
We might experience a connection 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.
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.
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.
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.
We use questions as tools to help us organize our thoughts.
While there is certainly a pragmatic side to questions, 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 with them 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