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A block diagonal matrix, also called a diagonal block matrix, is a square diagonal matrix in which the diagonal elements are square matrices of any size (possibly even 1×1), ...

The term Borel hierarchy is used to describe a collection of subsets of R defined inductively as follows: Level one consists of all open and closed subsets of R, and upon ...

A function f(x) is said to have bounded variation if, over the closed interval x in [a,b], there exists an M such that |f(x_1)-f(a)|+|f(x_2)-f(x_1)|+... +|f(b)-f(x_(n-1))|<=M ...

The word canonical is used to indicate a particular choice from of a number of possible conventions. This convention allows a mathematical object or class of objects to be ...

Catalan's triangle is the number triangle 1 ; 1 1 ; 1 2 2 ; 1 3 5 5 ; 1 4 9 14 14 ; 1 5 14 28 42 42 ; 1 6 20 48 90 132 132 (1) (OEIS A009766) with entries given by ...

An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f degreesg is differentiable at x. Furthermore, let y=f(g(x)) and u=g(x), then ...

Every "large" even number may be written as 2n=p+m where p is a prime and m in P union P_2 is the set of primes P and semiprimes P_2.

Church proved several important theorems that now go by the name Church's theorem. One of Church's theorems states that there is no consistent decidable extension of Peano ...

The circular points at infinity, also called the isotropic points, are the pair of (complex) points on the line at infinity through which all circles pass. The circular ...