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The theorem in set theory and logic that for all sets A and B, B=(A intersection B^_) union (B intersection A^_)<=>A=emptyset, (1) where A^_ denotes complement set of A and ...

Let U=(U,<··>) be a T2 associative inner product space over the field C of complex numbers with completion H, and assume that U comes with an antilinear involution xi|->xi^* ...

Let L be a language of first-order predicate logic, let I be an indexing set, and for each i in I, let A_i be a structure of the language L. Let u be an ultrafilter in the ...

A nonzero element x of a ring for which x·y=0, where y is some other nonzero element and the multiplication x·y is the multiplication of the ring. A ring with no zero ...

An algebra <L; ^ , v > is called a lattice if L is a nonempty set, ^ and v are binary operations on L, both ^ and v are idempotent, commutative, and associative, and they ...

In December 1920, M. Schönfinkel presented in a report to the Mathematical Society in Göttingen a new type of formal logic based on the concept of a generalized function ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...

Consider an n×n (0, 1)-matrix such as [a_(11) a_(23) ; a_(22) a_(34); a_(21) a_(33) ; a_(32) a_(44); a_(31) a_(43) ; a_(42) a_(54); a_(41) a_(53) ; a_(52) a_(64)] (1) for ...

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

There are a number of mathematical curves that produced heart shapes, some of which are illustrated above. A "zeroth" curve is a rotated cardioid (whose name means ...