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:
“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)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)