OFFSET
1,2
COMMENTS
Used as an example in the Schaffter link to support Cantor's diagonal argument. Most probably irrational and possible normal.
REFERENCES
Martin Aigner and Günter M. Ziegler, Proofs from THE BOOK, Second Edition, Springer-Verlag, Berlin Heidelberg NY, Section of Analysis, Chptr 15, "Sets, function, and the continuum hypothesis", 2000, pp. 87 - 98.
Georg Cantor, Über eine Eigenschaft des Inbegriffes aller reellen Zahlen ("On the Characteristic Property of All Real Numbers")
Timothy Gowers, Editor, with June Barrow-Green & Imre Leader, Assc. Editors, The Princeton Companion to Mathematics, Princeton Un. Press, Princeton & Oxford, 2008, pp. 171 & 779
Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §7.5 Transfinite Numbers, pp. 257-262.
LINKS
Richard Lipton, Gödel's Lost Letter and P=NP
Luke Mastin, 19th Century Mathematics - Cantor
Tom Schaffter, Cantor's Diagonal Argument: Proof and Paradox
Eric Weisstein's World of Mathematics, Cantor Diagonal Method
Wikipedia, Cantor's diagonal argument
FORMULA
EXAMPLE
The first decimal digit of 0 is 0, the second decimal digit of 1 (=0.99999...) is 9, the third decimal digit of 1/2 is 0, the fourth decimal digit of 1/3 is 3, the fifth decimal digit of 2/3 is 6, ..., the twelfth decimal digit of 1/6 is 6, the thirteenth decimal digit of 5/6 is 3, the fourteenth decimaldigit of 1/7 is 4, ..., .
MATHEMATICA
FareyOrder[n_] := Select[ Table[a/n, {a, n}], Denominator[#] == n &]; lst = Join[{0, .999999}, Flatten[ Table[ FareyOrder[n], {n, 2, 19}]]]; f[n_] := RealDigits[ lst[[n]], 10, 2 n][[1, n]]; Array[f, 105]
CROSSREFS
KEYWORD
easy,base,nonn
AUTHOR
Robert G. Wilson v, Mar 14 2013
STATUS
approved