Density
From Polymath1Wiki
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 
is a subset of [3]n then its density is 
One speaks loosely of a set ![\mathcal{A}\subset[3]^n](/polymath1/images/math/9/e/6/9e633bdf6026546cc8df6a7f4d2ae432.png)
being dense if its density δ 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 [3]n, such as equal-slices density. Then the words "density" and "dense" have obviously analogous uses.
