In the problem
The Cantor Set,
we met the Cantor set, which is the limit of
as
tends to infinity.
We can talk about the length of one of our sets
.
The set
has length 1.
The set
has length
, as this is the total
length of the line segments in
.
What are the lengths of
,
and
?
Can you find a general expression for the length of
?
By considering what happens as
tends to infinity, can you find the
length of the Cantor set?
