Definition
A positive irrational number generates the Beatty sequence
If then is also a positive irrational number. They naturally satisfy
and the sequences
- and
form a pair of complementary Beatty sequences.
A more general non-homogeneous Beatty sequence takes the form
where is a real number. For, the complementary non-homogeneous Beatty sequences can be found by making so that
- and
form a pair of complementary Beatty sequences. For other values of the procedure for finding complementary sequences is not as straightforward.
Read more about this topic: Beatty Sequence
Famous quotes containing the word definition:
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)