Question

Determine whether each of these sets is countable or uncountable.

(a) all bit strings that is finite.
(b) all bit strings that is infinite
(c) the real numbers containing a finite number of 1s in their decimal
representation (reminder: the real numbers can contain a infinite
number of 2s or 3s)
(d) the real numbers containing only 1s in their decimal representation

Answer 1

(a) All bit strings that are finite are countable.
(b) All bit strings that are infinite are uncountable.
(c) The real numbers containing a finite number of 1s in their decimal representation are countable.
(d) The real numbers containing only 1s in their decimal representation are uncountable.