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)
“Most of our occupations are low comedy.... We must play our part duly, but as the part of a borrowed character. Of the mask and appearance we must not make a real essence, nor of what is foreign what is our very own.”
—Michel de Montaigne (1533–1592)
“God ... created a number of possibilities in case some of his prototypes failed—that is the meaning of evolution.”
—Graham Greene (1904–1991)