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Brocard's problem asks to find the values of n for which n!+1 is a square number m^2, where n! is the factorial (Brocard 1876, 1885). The only known solutions are n=4, 5, and ...

A pair of consecutive numbers.

A puzzle in logic in which one or more facts must be inferred from a set of given facts.

The study of map projections and the making of geographical maps.

A Z-action or N-action. A cascade and a single map X->X are essentially the same, but the term "cascade" is preferred by many Russian authors.

A necessary and sufficient condition for a sequence S_i to converge. The Cauchy criterion is satisfied when, for all epsilon>0, there is a fixed number N such that ...

The geometric mean is smaller than the arithmetic mean, (product_(i=1)^Nn_i)^(1/N)<=(sum_(i=1)^(N)n_i)/N, with equality in the cases (1) N=1 or (2) n_i=n_j for all i,j.

The direct limit of the cohomology groups with coefficients in an Abelian group of certain coverings of a topological space.

The function [x] which gives the smallest integer >=x, shown as the thick curve in the above plot. Schroeder (1991) calls the ceiling function symbols the "gallows" because ...

A cellular space is a T2-space that has the structure of a so-called CW-complex.