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A nonempty finite set of n×n integer matrices for which there exists some product of the matrices in the set which is equal to the zero matrix.

A set that is a smooth embedded two-dimensional manifold except for a subset that consists of smooth embedded curves, except for a set of isolated points.

Quantifies deviation from translational invariance by describing the distribution of gaps within a set at multiple scales. The more lacunar a set, the more heterogeneous the ...

The set P^2 is the set of all equivalence classes [a,b,c] of ordered triples (a,b,c) in C^3\(0,0,0) under the equivalence relation (a,b,c)∼(a^',b^',c^') if ...

For a countable set of n disjoint events E_1, E_2, ..., E_n P( union _(i=1)^nE_i)=sum_(i=1)^nP(E_i).

Suppose <= is a partial ordering on a nonempty set A. Then the elements a,b in A are said to be comparable provided a<=b or b<=a. Because two elements in a partially ordered ...

Each point in the convex hull of a set S in R^n is in the convex combination of n+1 or fewer points of S.

A set X is a called a "convex cone" if for any x,y in X and any scalars a>=0 and b>=0, ax+by in X.

A set is said to be bounded from above if it has an upper bound. Consider the real numbers with their usual order. Then for any set M subset= R, the supremum supM exists (in ...

A set is said to be bounded from below if it has a lower bound. Consider the real numbers with their usual order. Then for any set M subset= R, the infimum infM exists (in R) ...