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Three elements x, y and z of a set S are said to be associative under a binary operation * if they satisfy x*(y*z)=(x*y)*z. (1) Real numbers are associative under addition ...

Axiomatic set theory is a version of set theory in which axioms are taken as uninterpreted rather than as formalizations of pre-existing truths.

A graph with graph edges of two possible "colors," usually identified as red and blue. For a bichromatic graph with R red graph edges and B blue graph edges, R+B>=2.

The smallest unit of binary information, equal to a single 0 or 1. Two bits are called a crumb, four bits are called a nibble, and eight bits are called 1 byte.

A point which is a member of the set closure of a given set S and the set closure of its complement set. If A is a subset of R^n, then a point x in R^n is a boundary point of ...

The boustrophedon ("ox-plowing") transform b of a sequence a is given by b_n = sum_(k=0)^(n)(n; k)a_kE_(n-k) (1) a_n = sum_(k=0)^(n)(-1)^(n-k)(n; k)b_kE_(n-k) (2) for n>=0, ...

The series producing Brun's constant converges even if there are an infinite number of twin primes, first proved by Brun (1919).

The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

A change of basis is the transformation of coordinate-based vector and operator representations in a given vector space from one vector basis representation to another.

The partial differential equation u_(xx)+(y^2)/(1-(y^2)/(c^2))u_(yy)+yu_y=0.