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The reflexive closure of a binary relation R on a set X is the minimal reflexive relation R^' on X that contains R. Thus aR^'a for every element a of X and aR^'b for distinct ...

Consider a countable subgroup H with elements h_i and an element x not in H, then h_ix for i=1, 2, ... constitute the right coset of the subgroup H with respect to x.

Let H be a subgroup of G. A subset T of elements of G is called a right transversal of H if T contains exactly one element of each right coset of H.

A set having exactly one element a. A singleton set is denoted by {a} and is the simplest example of a nonempty set.

The maximum cardinal number of a collection of subsets of a t-element set T, none of which contains another, is the binomial coefficient (t; |_t/2_|), where |_x_| is the ...

Also known as the total curvature. The linear element of the indicatrix ds_P=sqrt(ds_T^2+ds_B^2).

The subset {0} of a ring. It trivially fulfils the definition of ideal since it is a group (specifically, the zero group), and it is closed under multiplication by any ...

Ueberhuber (1997, p. 71) and Krommer and Ueberhuber (1998, pp. 49 and 155-165) use the word "quadrature" to mean numerical computation of a univariate integral, and ...

The smallest value of a set, function, etc. The minimum value of a set of elements A={a_i}_(i=1)^N is denoted minA or min_(i)a_i, and is equal to the first element of a ...

Let A={A_1,A_2,...,A_n} be a union-closed set, then the union-closed set conjecture states that an element exists which belongs to at least n/2 of the sets in A. Sarvate and ...