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A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset). Members of a ...

A (-1,0,1)-matrix is a matrix whose elements consist only of the numbers -1, 0, or 1. The number of distinct (-1,0,1)-n×n matrices (counting row and column permutations, the ...

The number 10 (ten) is the basis for the decimal system of notation. In this system, each "decimal place" consists of a digit 0-9 arranged such that each digit is multiplied ...

1729 is sometimes called the Hardy-Ramanujan number. It is the smallest taxicab number, i.e., the smallest number which can be expressed as the sum of two cubes in two ...

65537 is the largest known Fermat prime, and the 65537-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. The 65537-gon has so many ...

An infinite sequence of positive integers a_i satisfying 1<=a_1<a_2<a_3<... (1) is an A-sequence if no a_k is the sum of two or more distinct earlier terms (Guy 1994). Such ...

A connective in logic which yields true if all conditions are true, and false if any condition is false. A AND B is denoted A ^ B (Mendelson 1997, p. 12), A&B, A intersection ...

A mechanical counting device consisting of a frame holding a series of parallel rods on each of which beads are strung. Each bead represents a counting unit, and each rod a ...

The following integral transform relationship, known as the Abel transform, exists between two functions f(x) and g(t) for 0<alpha<1, f(x) = int_0^x(g(t)dt)/((x-t)^alpha) (1) ...

A real number that is b-normal for every base 2, 3, 4, ... is said to be absolutely normal. As proved by Borel (1922, p. 198), almost all real numbers in [0,1) are absolutely ...