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)
“Thoughtfulness for others, generosity, modesty, and self- respect, are the qualities which make a real gentleman, or lady, as distinguished from the veneered article which commonly goes by that name.”
—Thomas Henry Huxley (1825–95)
“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)