منابع مشابه
A note on normal numbers
Many cyberinformaticians would agree that, had it not been for the transistor, the construction of link-level acknowledgements might never have occurred. Given the current status of probabilistic modalities, electrical engineers obviously desire the improvement of rasterization, which embodies the structured principles of robotics. In this position paper, we concentrate our efforts on verifying...
متن کاملNormal Numbers Are Normal
A number is normal in base b if every sequence of k symbols in the letters 0, 1, . . . , b− 1 occurs in the base-b expansion of the given number with the expected frequency b−k. From an informal point of view, we can think of numbers normal in base 2 as those produced by flipping a fair coin, recording 1 for heads and 0 for tails. Normal numbers are those which are normal in every base. In this...
متن کاملOn Normal Numbers and Powers of Algebraic Numbers
Let α > 1 be an algebraic number and ξ > 0. Denote the fractional parts of ξαn by {ξαn}. In this paper, we estimate a lower bound for the number λN (α, ξ) of integers n with 0 ≤ n < N and {ξα} ≥ min { 1 L+(α) , 1 L−(α) } . Our results show, for example, the following: Let α be an algebraic integer with Mahler measure M(α) and ξ > 0 an algebraic number with ξ #∈ Q(α). Put [Q(α, ξ) : Q(α)] = D. T...
متن کاملOn Simply Normal Numbers to Different Bases
Let s be an integer greater than or equal to 2. A real number is simply normal to base s if in its base-s expansion every digit 0, 1, . . . , s ́ 1 occurs with the same frequency 1{s. Let S be the set of positive integers that are not perfect powers, hence S is the set t2, 3, 5, 6, 7, 10, 11, . . .u. Let M be a function from S to sets of positive integers such that, for each s in S, if m is in M...
متن کاملOn the Normality of Normal Numbers
where # denotes cardinality. Equation (1) characterizes some, but not all, numbers between zero and one. For example, x = 0 and x = 1 do not satisfy (1), and the following do: 0.10101010 · · · , 0.01010101 · · · , 0.001001001 · · · , etc. We can observe that the preceding three examples are all “periodic.” Thus, one can ask if there are numbers that satisfy (1) whose digits are not periodic. Bo...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1960
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1960.10.661