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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 ...

The wreathed product of the monster group by Z_2. The bimonster is a quotient of the Coxeter group with the above Coxeter-Dynkin diagram. This had been conjectured by Conway, ...

The conditional probability of an event A assuming that B has occurred, denoted P(A|B), equals P(A|B)=(P(A intersection B))/(P(B)), (1) which can be proven directly using a ...

An exmedian is a parallel to a side of a triangle through the opposite vertex. So in the above diagram, A_2^'A_3^' is the exmedian of side A_2A_3, and so on. The pairwise ...

The squeeze theorem, also known as the squeezing theorem, pinching theorem, or sandwich theorem, may be stated as follows. Let there be two functions f_-(x) and f_+(x) such ...

The connective in logic corresponding to the exclusive nor operation. A XNOR B is equivalent to (A ^ B) v (!A ^ !B), where ^ denotes AND, v denotes OR, and !A denotes NOT. ...

The connective in logic corresponding to the exclusive nor operation. A XNOR B is equivalent to (A ^ B) v (!A ^ !B), where ^ denotes AND, v denotes OR, and !A denotes NOT. ...

A short exact sequence of groups 0-->A-->B-->C-->0 (1) is called split if it essentially presents B as the direct sum of the groups A and C. More precisely, one can construct ...

There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal ...

A plane partition whose solid Ferrers diagram is invariant under the rotation which cyclically permutes the x-, y-, and z-axes. Macdonald's plane partition conjecture gives a ...