Wikipedia says "In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it" (https://en.wikipedia.org/wiki/Dimension).
However, this is a vague definition.
In fact, one could represent "2-dimensional" space with only a singular coordinate.
For example, consider the 2-D polar coordinates (r, θ) in R2; θ is in radians. We can then create a single number C such that the even digits of C are the digits of r, and the odd digits of C are the digits of θ. There is a 1-to-1 mapping between (r, θ) and C.
So, what is a precise and accurate definition of "dimension"? Do we think about dimensions the wrong way? What is so inherent about the way we think about dimensions?