Normal recurring decimals, normal periodic systems, (j,ε) - normality, and normal numbers
نویسندگان
چکیده
منابع مشابه
Normal numbers and normality measure
The normality measure N has been introduced by Mauduit and Sárközy in order to describe the pseudorandomness properties of finite binary sequences. Alon, Kohayakawa, Mauduit, Moreira and Rödl proved that the minimal possible value of the normality measure of an N -element binary sequence satisfies
متن کاملNormal Numbers and the Normality Measure
In a paper published in this journal, Alon, Kohayakawa, Mauduit, Moreira, and Rödl proved that the minimal possible value of the normality measure of an N -element binary sequence satisfies ( 1 2 + o(1) ) log2N ≤ min EN∈{0,1} N (EN ) ≤ 3N(logN) for sufficiently large N , and conjectured that the lower bound can be improved to some power of N . In this note it is observed that a construction of ...
متن کاملNote on Normal Decimals
It was proved by Champernowne [2] that the decimal . 1234567891011 . . . is normal, and by Besicovitch [11 that the same holds for the decimal . 1491625 . . . . Copeland and Erdös [3] have proved that if p i, P2 . . . . is any sequence of positive integers such that, for every 0 < 1, the number of p's up to n exceeds nB if n is sufficiently large, then the infinite decimal •p ip 2p 3 . . . is n...
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...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1976
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-28-4-349-361