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)
“A real life, a life that leaves a deposit in the shape of something alive.... It’s difficult to say what makes a life a real life.... You could also say it depends on a person being identical with himself.”
—Max Frisch (1911–1991)
“The two great points of difference between a democracy and a republic are: first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens and greater sphere of country over which the latter may be extended.”
—James Madison (1751–1836)