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:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)