|
Two nonnegative reduced fractions  and  make a Farey pair (with  ) whenever  , in other words, they are a Farey pair if their difference is  .
The interval ![$[a/b, c/d]$](http://images.planetmath.org:8080/cache/objects/6597/l2h/img6.png "$[a/b, c/d]$") is known as a Farey interval.
Given a Farey pair  , their mediant is  . The mediant has the following property:
If ![$[a,b,c/d]$](http://images.planetmath.org:8080/cache/objects/6597/l2h/img9.png "$[a,b,c/d]$") is a Farey interval, then the two subintervals obtained when inserting the mediant are also Farey pairs. Besides, between all fractions that are strictly between  , the mediant is the one having the smallest denominator.
Example.
Notice that  and  form a Farey pair, since
 . The mediant here is  .
Then  and  form a Farey pair:
 . No fraction between  and  other than  has a denominator smaller or equal than  .
| 
