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The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.

If n>19, there exists a Poulet number between n and n^2. The theorem was proved in 1965.

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

A degree set is a set of integers that make up a degree sequence. Any set of positive integers is the degree set for some graph, because any odd integer from that set can be ...

Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

The Frobenius equation is the Diophantine equation a_1x_1+a_2x_2+...+a_nx_n=b, where the a_i are positive integers, b is an integer, and the solutions x_i are nonnegative ...

A Størmer number is a positive integer n for which the greatest prime factor p of n^2+1 is at least 2n. Every Gregory number t_x can be expressed uniquely as a sum of t_ns ...

A number of the form Tt_n=((n+2; 2); 2)=1/8n(n+1)(n+2)(n+3) (Comtet 1974, Stanley 1999), where (n; k) is a binomial coefficient. The first few values are 3, 15, 45, 105, 210, ...

Liouville's constant, sometimes also called Liouville's number, is the real number defined by L=sum_(n=1)^infty10^(-n!)=0.110001000000000000000001... (OEIS A012245). ...

A pseudoprime is a composite number that passes a test or sequence of tests that fail for most composite numbers. Unfortunately, some authors drop the "composite" ...