A quotation:

There are an infinite number of points in the Cantor set. There are also an infinite number of points within the original line segment which are not in the Cantor set. Both of these numbers are equally large (in technical terms, they have the same cardinality), and both are as large as the number of points in the original line segment. The Cantor set is an infinite number of points spread over a finite line segment which, combined, have 0 length.