Automatic Sequence - Automatic Real Number

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:

    The ruin of the human heart is self-interest, which the American merchant calls self-service. We have become a self- service populace, and all our specious comforts—the automatic elevator, the escalator, the cafeteria—are depriving us of volition and moral and physical energy.
    Edward Dahlberg (1900–1977)

    Nobody of any real culture, for instance, ever talks nowadays about the beauty of sunset. Sunsets are quite old fashioned.... To admire them is a distinct sign of provincialism of temperament. Upon the other hand they go on.
    Oscar Wilde (1854–1900)

    One may confidently assert that when thirty thousand men fight a pitched battle against an equal number of troops, there are about twenty thousand on each side with the pox.
    Voltaire [François Marie Arouet] (1694–1778)