Dimension is not a single concept. There are many conflicting possibilities for the definition of dimension.

1. The number of coordinates.

2. If a d-1 dimensional closed barrier can be placed between any two points of X then we say X is d-dimensional. This is the inductive dimensional of a set, Brouwer.

3. A finite cover of open sets exists which satisfy three coverage properties.

4. There are homological and cohomological definitions. The homological definition is the largest d for which some substructure of X has a nontrivial d-th homology group. This definition can be extended to groups and rings.

5. The number that corresponds to the best measure of size, such as, length, area, volume and non-integer extensions of these.

The Cantor set is defined by removing middle thirds of the closed interval from zero to one.

A typographical mistake was found. 1/3 can be written as 0.1 or 0.02222… in ternary expansions. Not as “0.22222…” which is equal to 1.0.