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)
“When I read of the vain discussions of the present day about the Virgin Birth and other old dogmas which belong to the past, I feel how great the need is still of a real interest in the religion which builds up character, teaches brotherly love, and opens up to the seeker such a world of usefulness and the beauty of holiness.”
—Olympia Brown (1835–1900)
“Strange goings on! Jones did it slowly, deliberately, in the bathroom, with a knife, at midnight. What he did was butter a piece of toast. We are too familiar with the language of action to notice at first an anomaly: the ‘it’ of ‘Jones did it slowly, deliberately,...’ seems to refer to some entity, presumably an action, that is then characterized in a number of ways.”
—Donald Davidson (b. 1917)