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A prime ideal is an ideal I such that if ab in I, then either a in I or b in I. For example, in the integers, the ideal a=<p> (i.e., the multiples of p) is prime whenever p ...

A proof by contradiction establishes the truth of a given proposition by the supposition that it is false and the subsequent drawing of a conclusion that is contradictory to ...

If proofreader A finds a mistakes and proofreader B finds b mistakes, c of which were also found by A, how many mistakes were missed by both A and B? Assume there are a total ...

A tree having four branches at each node. Quadtrees are used in the construction of some multidimensional databases (e.g., cartography, computer graphics, and image ...

A positive number k such that a lamina or solid body with moment of inertia about an axis I and mass m is given by I=mk^2. Pickover (1995) defines a generalization of k as a ...

Ramsey's theorem is a generalization of Dilworth's lemma which states for each pair of positive integers k and l there exists an integer R(k,l) (known as the Ramsey number) ...

Let the true value of a quantity be x and the measured or inferred value x_0. Then the relative error is defined by deltax=(Deltax)/x=(x_0-x)/x=(x_0)/x-1, where Deltax is the ...

In general, a remainder is a quantity "left over" after performing a particular algorithm. The term is most commonly used to refer to the number left over when two integers ...

A tree of links obtained by repeatedly choosing a crossing, applying the skein relationship to obtain two simpler links, and repeating the process. The tree depth of a ...

There is a one-to-one correspondence between the sets of equivalent correspondences (not of value 0) on an irreducible curve of curve genus p, and the rational collineations ...