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A map is called bijective if it is both injective and surjective. A bijective map is also called a bijection. A function f admits an inverse f^(-1) (i.e., "f is invertible") ...

Every Boolean algebra is isomorphic to the Boolean algebra of sets. The theorem is equivalent to the maximal ideal theorem, which can be proved without using the axiom of ...

A product of ANDs, denoted ^ _(k=1)^nA_k. The conjunctions of a Boolean algebra A of subsets of cardinality p are the 2^p functions A_lambda= union _(i in lambda)A_i, where ...

Given a sequence of real numbers a_n, the infimum limit (also called the limit inferior or lower limit), written lim inf and pronounced 'lim-inf,' is the limit of ...

Model completion is a term employed when existential closure is successful. The formation of the complex numbers, and the move from affine to projective geometry, are ...

Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...

Pre-Calculus

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

A lattice which satisfies the identities (x ^ y) v (x ^ z)=x ^ (y v z) (x v y) ^ (x v z)=x v (y ^ z) is said to be distributive.

A lattice which satisfies the identity (x ^ y) v (x ^ z)=x ^ (y v (x ^ z)) is said to be modular.