User blog:Holomanga/A Thought On Dimensionality

If you have two sets A and B, and you want to describe the location of an element of B using some number of elements of A, you need an ordered tuple at least

$$\lceil \text{log}_{|A|}|B| \rceil$$

elements of A. This is the minimum dimensionality of B when coordinates of elements of B can take values from A.