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A method of constructing uniform polyhedra.

The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...

In general, groups are not Abelian. However, there is always a group homomorphism h:G->G^' to an Abelian group, and this homomorphism is called Abelianization. The ...

An algebraic group is a variety (or scheme) endowed with a group structure such that the group operations are morphisms of varieties (or schemes). The concept is similar to ...

Let A and B_j be sets. Conditional probability requires that P(A intersection B_j)=P(A)P(B_j|A), (1) where intersection denotes intersection ("and"), and also that P(A ...

Let A and B be any sets with empty intersection, and let |X| denote the cardinal number of a set X. Then |A|+|B|=|A union B| (Ciesielski 1997, p. 68; Dauben 1990, p. 173; ...

Let A and B be any sets, and let |X| be the cardinal number of a set X. Then cardinal exponentiation is defined by |A|^(|B|)=|set of all functions from B into A| (Ciesielski ...

Let A and B be any sets. Then the product of |A| and |B| is defined as the Cartesian product |A|*|B|=|A×B| (Ciesielski 1997, p. 68; Dauben 1990, p. 173; Moore 1982, p. 37; ...

The product of a family {X_i}_(i in I) of objects of a category is an object P=product_(i in I)X_i, together with a family of morphisms {p_i:P->X_i}_(i in I) such that for ...

Let m(G) be the cycle rank of a graph G, m^*(G) be the cocycle rank, and the relative complement G-H of a subgraph H of G be defined as that subgraph obtained by deleting the ...