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:
“Natural selection, the blind, unconscious, automatic process which Darwin discovered, and which we now know is the explanation for the existence and apparently purposeful form of all life, has no purpose in mind. It has no mind and no mind’s eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of the watchmaker in nature, it is the blind watchmaker.”
—Richard Dawkins (b. 1941)
“Only men of moral and mental force, of a patriotic regard for the relationship of the two races, can be of real service as ministers in the South. Less theology and more of human brotherhood, less declamation and more common sense and love for truth, must be the qualifications of the new ministry that shall yet save the race from the evils of false teaching.”
—Fannie Barrier Williams (1855–1944)
“There is something tragic about the enormous number of young men there are in England at the present moment who start life with perfect profiles, and end by adopting some useful profession.”
—Oscar Wilde (1854–1900)