An automatic real number is a real number for which the base-b expansion is an automatic sequence. All such numbers are either rational or transcendental, but not a U-number. Rational numbers are k-automatic in base b for all k and b.
Read more about this topic: Automatic Sequence
Famous quotes containing the words automatic, real and/or number:
“She smoothes her hair with automatic hand,
And puts a record on the gramophone.”
—T.S. (Thomas Stearns)
“No good poetry is ever written in a manner twenty years old, for to write in such a manner shows conclusively that the writer thinks from books, convention and cliché, not from real life.”
—Ezra Pound (1885–1972)
“Nothing ever prepares a couple for having a baby, especially the first one. And even baby number two or three, the surprises and challenges, the cosmic curve balls, keep on coming. We can’t believe how much children change everything—the time we rise and the time we go to bed; the way we fight and the way we get along. Even when, and if, we make love.”
—Susan Lapinski (20th century)