The Cantor set
is constructed iteratively. Starting with the closed unit interval
, the open middle third
is taken out, leaving the two closed intervals
and
. Then the middle thirds of those two intervals are taken out, leaving four intervals of length
, and so on. The Cantor set is the limit (or intersection) of all such sets.
Even though the Cantor set has measure zero and is nowhere dense, the set of sums
where
and
are in
is the whole interval
, because the line
always intersects the set
.
Browse all topics
