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A function f mapping a set X->X/R (X modulo R), where R is an equivalence relation in X, is called a canonical map.

The points on a line can be put into a one-to-one correspondence with the real numbers.

omega^epsilon=epsilon, where omega is an ordinal number and epsilon is an inaccessible cardinal.

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 ...

The 6-polyiamond illustrated above.