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The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers aleph_0 and the "large" ...

A real-linear vector space H equipped with a symplectic form s.

The triangle of numbers A_(n,k) given by A_(n,1)=A_(n,n)=1 (1) and the recurrence relation A_(n+1,k)=kA_(n,k)+(n+2-k)A_(n,k-1) (2) for k in [2,n], where A_(n,k) are shifted ...

Decimal is the base-10 notational system for representing real numbers. The expression of a number using the decimal system is called its decimal expansion, examples of which ...

An n-step Lucas sequence {L_k^((n))}_(k=1)^infty is defined by letting L_k^((n))=-1 for k<0, L_0^((n))=n, and other terms according to the linear recurrence equation ...

An integer N which is a product of distinct primes and which satisfies 1/N+sum_(p|N)1/p=1 (Butske et al. 1999). The first few are 2, 6, 42, 1806, 47058, ... (OEIS A054377). ...

Catalan (1876, 1891) noted that the sequence of Mersenne numbers 2^2-1=3, 2^3-1=7, and 2^7-1=127, and (OEIS A007013) were all prime (Dickson 2005, p. 22). Therefore, the ...

Aleph-1 is the set theory symbol aleph_1 for the smallest infinite set larger than aleph_0 (Aleph-0), which in turn is equal to the cardinal number of the set of countable ...

A Trott constant is a real number whose decimal digits are equal to the terms of its continued fraction. The first Trott constant (OEIS A039662) was discovered by M. Trott in ...

An irreducible algebraic integer which has the property that, if it divides the product of two algebraic integers, then it divides at least one of the factors. 1 and -1 are ...