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.
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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)
“The real grounds of difference upon important political questions no longer correspond with party lines.... Politics is no longer the topic of this country. Its important questions are settled... Great minds hereafter are to be employed on other matters.... Government no longer has its ancient importance.... The people’s progress, progress of every sort, no longer depends on government. But enough of politics. Henceforth I am out more than ever.”
—Rutherford Birchard Hayes (1822–1893)
“Today, almost forty years later, I grow dizzy when I recall that the number of manufactured tanks seems to have been more important to me than the vanished victims of racism.”
—Albert Speer (1905–1981)