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A Cantor set Associated With Sierpiński's Algorithm
Author(s) -
Shiu P.
Publication year - 1995
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/27.1.75
Subject(s) - mathematics , cantor set , sierpinski triangle , sequence (biology) , set (abstract data type) , combinatorics , discrete mathematics , cantor's diagonal argument , algorithm , representation (politics) , uncountable set , infinite set , cantor function , fractal , mathematical analysis , countable set , computer science , biology , politics , law , political science , genetics , programming language
W. Sierpiński showed that each x in 0< x ⩽1 has a representation ∑1/ a 1 … a k is an increasing sequence of positive integers. We show that the subset of numbers x for which( a k ) is strictly increasing is a Cantor set.