The word density or dense has a variety of senses in the physical, mathematical, and quantitative sciences.
In Physics:
In Demographics:
In Computer science:
In Statistics:
In Pure Mathematics:
- Schnirelmann density in number theory
- natural density in number theory
- nowhere dense set and dense set in topology
- A partial order on a set S is said to be dense (or dense-in-itself) if, for all x and y in S for which x < y, there is a z in S such that x < z < y. The rational numbers with the ordinary ordering are a densely ordered set in this sense, as are the real numbers.
- In order theory, a subset B of a partially ordered set A is dense in A if for any x < y in A, there is some z in B such that x < z < y. In case the order is a linear order, then B is dense in A in the present sense if and only if B is dense in the order topology on A. Hence the first two meanings above are related.
- In forcing, a subset D of a forcing notion (P, ≤ ) is called dense in P if for any p in P there is d in D with d≤p. (Note: since a forcing notion is also a partial order, this usage of the word "dense" conflicts with the definition given above. However, the above notion of "density" is practically never used when talking about forcing notions, so any ambiguities are usually easily resolved from the context.)
Density, the band
- Density is also the name of a Italian progressive band. Their repertoire varies from the pub project (covers of Queen, Guns n'roses, Europe...) and their composition project (inspirations from Dream Theater, Extreme, Yes...). [1]
