Definition
Relation
A relation is a set of ordered pairs showing which first values pair with which second values.
What it means
Think of each ordered pair as a recorded match. In (2, 5), 2 is the first value and 5 is the value paired with it. All the recorded matches together make the relation.
Remember it
A relation is a list of first-goes-with-second matches.
Example
R = {(1, 3), (2, 5), (3, 7)} is a relation. It pairs 1 with 3, 2 with 5, and 3 with 7.
Watch for
A relation may pair one first value with more than one second value. If it does, the relation is not a function.
Common mix-up
Every function is a relation, but not every relation is a function.
Exact meaning
In algebra, a relation is a set of ordered pairs. Each ordered pair states that one value from the first set is paired with one value from the second set.