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The set theory symbol aleph_0 refers to a set having the same cardinal number as the "small" infinite set of integers. The symbol aleph_0 is often pronounced "aleph-null" ...

A Banach algebra is an algebra B over a field F endowed with a norm ||·|| such that B is a Banach space under the norm ||·|| and ||xy||<=||x||||y||. F is frequently taken to ...

The finite simple groups of Lie-type. They include four families of linear simple groups: PSL(n,q) (the projective special linear group), PSU(n,q) (the projective special ...

An integral obtained by contour integration. The particular path in the complex plane used to compute the integral is called a contour. As a result of a truly amazing ...

A topological space that is not connected, i.e., which can be decomposed as the disjoint union of two nonempty open subsets. Equivalently, it can be characterized as a space ...

The Euler-Gergonne-Soddy triangle is the right triangle DeltaZFlEv created by the pairwise intersections of the Euler line L_E, Soddy line L_S, and Gergonne line L_G. (The ...

A finitely presented group is a group with a finite number of generators and relations. A mathematical joke involving finitely presented groups is given by Renteln and Dundes ...

For all integers n and nonnegative integers t, the harmonic logarithms lambda_n^((t))(x) of order t and degree n are defined as the unique functions satisfying 1. ...

Let H_n denote the nth hexagonal number and S_m the mth square number, then a number which is both hexagonal and square satisfies the equation H_n=S_m, or n(2n-1)=m^2. (1) ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), define the Hilbert function of M as the map ...