Show that the shift map o : {0, 1}N → {0,1}N is continuous, where o(x) is e sequence obtained by throwing away the first symbol of z (so, for example, 10011010...) = 0011010...: we can define o precisely by o(1)n = In+1, %3D e. the nth symbol of o(x) is the n+ 1st symbol of r.)

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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** Show that the shift map o : {0,1}N → {0,1}N is continuous, where o(x) is
the sequence obtained by throwing away the first symbol of x (so, for example,
o(10011010...) = 0011010...: we can define o precisely by
%3D
o(1)n = In+11
%3D
i.e. the nth symbol of o(x) is the n+1st symbol of r.)
Transcribed Image Text:** Show that the shift map o : {0,1}N → {0,1}N is continuous, where o(x) is the sequence obtained by throwing away the first symbol of x (so, for example, o(10011010...) = 0011010...: we can define o precisely by %3D o(1)n = In+11 %3D i.e. the nth symbol of o(x) is the n+1st symbol of r.)
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