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The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...

The rank of a graph G is defined as r(G)=n-c, where n is the number of vertices on G and c is the number of connected components (Biggs 1993, p. 25).

As shown by Schur (1916), the Schur number S(n) satisfies S(n)<=R(n)-2 for n=1, 2, ..., where R(n) is a Ramsey number.

For a subgroup H of a group G, the index of H, denoted (G:H), is the cardinal number of the set of left cosets of H in G (which is equal to the cardinal number of the set of ...

An element of an extension field of a field F which is not algebraic over F. A transcendental number is a complex number which is transcendental over the field Q of rational ...

The real part R[z] of a complex number z=x+iy is the real number not multiplying i, so R[x+iy]=x. In terms of z itself, R[z]=1/2(z+z^_), where z^_ is the complex conjugate of ...

Infinity, most often denoted as infty, is an unbounded quantity that is greater than every real number. The symbol infty had been used as an alternative to M (1000) in Roman ...

The Galton board, also known as a quincunx or bean machine, is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of an ...

Quicksort is the fastest known comparison-based sorting algorithm (on average, and for a large number of elements), requiring O(nlgn) steps. Quicksort is a recursive ...