Sets are denoted by capital letters A, elements by lowercase letters a. Inclusion (⊂) means elements belong to set, proper inclusion (A B) means A is different from B. Empty set ∅ represents set with no elements
A set is a well-defined collection of objects, with elements being its members. Sets can be finite (empty or contain exactly n elements) or infinite. The empty set is a subset of every other set
Relations establish connections between elements of two sets. Relations are represented as ordered pairs (x, y). Relations are subsets of the cartesian product of two sets
Cartesian product of two sets A and B is the set of ordered pairs (a, b). Named after René Descartes, who developed it in analytic geometry. Not commutative and not associative unless one set is empty. Cardinality of product equals product of cardinalities of input sets
Cross product measures interactions between different dimensions of vectors. Dot product measures similarity between vectors in matching dimensions. Cross product requires 6 individual differences to calculate total difference
Cross product is a vector multiplication defined in 3D and 7D. Useful in physics and engineering applications