View source for Density

Let X be a finite set. The usual definition of the density of a subset Y of X is |Y|/|X|, that is, the size of Y divided by the size of X. In particular, if <math>\mathcal{A}</math> is a subset of <math>[3]^n</math> then its density is <math>3^{-n}|\mathcal{A}.</math> 

One speaks loosely of a set <math>\mathcal{A}\subset[3]^n</math> being ''dense'' if its density <math>\delta</math> is bounded below by a positive constant that is independent of n. Strictly speaking, this definition applies to sequences of sets with n tending to infinity, but it is a very useful way of talking.

Sometimes it is helpful to consider other probability measures on <math>[3]^n,</math> such as [[equal-slices_measure|equal-slices density]]. Then the words "density" and "dense" have obviously analogous uses.