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The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The ...

Consider a library which compiles a bibliographic catalog of all (and only those) catalogs which do not list themselves. Then does the library's catalog list itself?

The central factorials x^([k]) form an associated Sheffer sequence with f(t) = e^(t/2)-e^(-t/2) (1) = 2sinh(1/2t), (2) giving the generating function ...

A point v is a central point of a graph if the eccentricity of the point equals the graph radius. The set of all central points is called the graph center.

A point in a weighted tree that has minimum weight for the tree. The set of all centroid points is called a tree centroid (Harary 1994, p. 36). The largest possible values ...

A surface with tetrahedral symmetry which looks like an inflatable chair from the 1970s. It is given by the implicit equation The surface illustrated above has k=5, a=0.95, ...

The 6-polyiamond illustrated above.

A node which is one graph edge further away from a given node in a rooted tree.

An alternative term for a binomial coefficient, in which (n; k) is read as "n choose k." R. K. Guy suggested this pronunciation around 1950, when the notations ^nC_r and ...