Let l = {x: 0 = x = 1} be the unit interval in IR 1 and let every x ? I be represented in a…

Let l = {x: 0 = x = 1} be the unit interval in IR 1 and let every x ? I be represented in a…

Let l = {x: 0 ≤ x ≤ 1} be the unit interval in IR 1 and let every x ϵ I be represented in a ternary expansion:

where each a; has the value 0, 1, or 2. Let A be the subset of I such that every point of A has only zeros or twos in its expansion.

(a) Show that A is an uncountable set.

(b) Show that A is nowhere dense in I.

 

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