A Cantor set Associated With Sierpiński's Algorithm | Zendy

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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.

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