Various parts of mathematics use a NULL-like concept. The ones which to me seem to be the closest to the NULL of relational databases crop up in Chris Strachey and Dana Scott's denotational semantics for programmes where one can have values like "bottom of D" for each domain D, and of course "bottom" for "bottom of everything". Basically "bottom of D" is a value in D of which we know nothing but that it is in D, while "bottom" is a value of which we know nothing, not even what domain it is a member of. Essentially all values exist in a lattice, and each domain is a sublattice, with the < relation in the lattice meaning "is less well defined". There is also a top value, which is overdefined (ie is contradictory), and potentially "top of D" values which are also overdefined but slightly less so (non-contradictory information on which domain they are in is available). Of course bottom and top occur naturally in lattice theory, even before it is applied to the denotational semantics of programmmes. But if one considers the natural topology of the lattices used in denotational semantics you see that the meaning of a recursive programme is the limit of the meanings of its partial evaluations (eg the meaning of a programme that computes factorials is the limit of the series of meanings of the programmes F(N) that produce factorials for numbers up to N but don't deliver a result for numbers > N, as N increases), which is quite a strong constraint on the lattices.

Despite the closeness of the NULLs of RDBMS with the bottoms of Scott-Strachey semantics, and the fact that both indicate an absence of knowledge about a value, they are conceptually quite different.

edit:correct the English