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If S is an infinite set, then the collection F_S={A subset= S:S-A is finite} is a filter called the cofinite (or Fréchet) filter on S.

In mathematics, the term "collection" is generally used to mean a multiset, i.e., a set in which order is ignored but multiplicity is significant.

Complete digraphs are digraphs in which every pair of nodes is connected by a bidirectional edge.

The graph corresponding to the complete k-ary tree on n nodes is implemented in the Wolfram Language as KaryTree[n, k].

A group L is a component of H if L is a quasisimple group which is a subnormal subgroup of H.

A concordance between knots K_0 and K_1 in S^3 is a locally flat cylinder C=S^1×[0,1] embedded in S^3×[0,1] in such a way that the ends S^1×{1} are embedded in S^3×{i} as ...

Given a group with elements A and X, there must be an element B which is a similarity transformation of A,B=X^(-1)AX so A and B are conjugate with respect to X. Conjugate ...

A subgroup H of an original group G has elements h_i. Let x be a fixed element of the original group G which is not a member of H. Then the transformation xh_ix^(-1), (i=1, ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

A functor F is called contravariant if it reverses the directions of arrows, i.e., every arrow f:A-->B is mapped to an arrow F(f):F(B)-->F(A).