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A loose term for a true statement which may be a postulate, theorem, etc.

If 0<=a,b,c,d<=1, then (1-a)(1-b)(1-c)(1-d)+a+b+c+d>=1. This is a special case of the general inequality product_(i=1)^n(1-a_i)+sum_(i=1)^na_i>=1 for 0<=a_1,a_2,...,a_n<=1. ...

A recursive process is one in which objects are defined in terms of other objects of the same type. Using some sort of recurrence relation, the entire class of objects can ...

A recursive sequence {f(n)}_n, also known as a recurrence sequence, is a sequence of numbers f(n) indexed by an integer n and generated by solving a recurrence equation. The ...

The Riemann integral is the definite integral normally encountered in calculus texts and used by physicists and engineers. Other types of integrals exist (e.g., the Lebesgue ...

Gram-Schmidt orthogonalization, also called the Gram-Schmidt process, is a procedure which takes a nonorthogonal set of linearly independent functions and constructs an ...

A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that has been proven is called a theorem. ...

1. Zero is a number. 2. If a is a number, the successor of a is a number. 3. zero is not the successor of a number. 4. Two numbers of which the successors are equal are ...

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in ...

One of the Zermelo-Fraenkel axioms, also known as the axiom of regularity (Rubin 1967, Suppes 1972). In the formal language of set theory, it states that x!=emptyset=> exists ...